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Ha, tells you if the test is left, right, or two-tailed. It is the key to conducting the appropriate test. • Ha never has a symbol that contains an equal sign. • Thinking about the meaning of the p-value: A data analyst should have more confidence that he made the correct decision to reject the null hypothesis with a ... |
| Hypothesis Testing with One Sample Full Hypothesis Test Examples Example 9.14 Jeffrey, as an eight-year-old, established a mean time of 16.43 seconds for swimming the 25-yard freestyle, with a standard deviation of 0.8 seconds. His dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster using goggle... |
value: α = 0.05 p-value = 0.0187 α > p-value This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 9 | Hypothesis Testing with One Sample 535 Make a decision: Since α > p-value, reject H0. An alternative approach is to find the z-test corresponding to the sample mean x¯ = 16. This is z... |
P( x¯ < 16) = 2nd DISTR normcdf ⎛ ⎝ − 10 ^ 99, 16, 16.43, 0.8 / 15⎞ ⎠. The Type I and Type II errors for this problem are as follows: The Type I error is to conclude that Jeffrey swims the 25-yard freestyle, on average, in less than 16.43 seconds when, in fact, he actually swims the 25-yard freestyle, on average, in 1... |
value, and the test statistic and the critical value. Figure 9.7 9.14 The mean throwing distance of a football by Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20 thr... |
This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 9 | Hypothesis Testing with One Sample 537 Since the problem is about a mean weight, this is a test of a single population mean. H0: μ = 275 Calculating the distribution needed: Ha: μ > 275 This is a right-tailed test. Random varia... |
55 for σ, the name of the list where you put the data, and the name of the list where you put the frequencies. Arrow down to μ: and arrow over to > μ0. Press ENTER. Arrow down to Calculate and press ENTER. The calculator not only calculates the p-value (p = 0.1331, a little different from the previous calculation—in i... |
μ X s X n = 67 − 65 3.12 10 ≈ 1.98. The p-value is the probability to the right tail of 1.98 in a t-distribution with nine degrees of freedom. p-value = P( x¯ > 67) = 0.0396 where the sample mean and sample standard deviation are calculated as 67 and 3.1972 from the data. Interpretation of the p-value: If the null hyp... |
0.0396 (p-value). Make sure when you use Draw that no other equations are highlighted in Y = and the plots are turned off. 9.16 It is believed that a stock price for a particular company will grow at a rate of $5 per week with a standard deviation of $1. An investor believes the stock won’t grow as quickly. The change... |
×0.50 100 = 0.6. is positive, we compute the area to the right Since the z-test tail of 0.6 in a normal distribution, P(Z > 0.6) = 0.2742531. Finally, because this is a two-sided test of significance, we multiply this probability times two to account for the left tail, and obtain () p-value = 2×0.2742531 = 0.5485062 wh... |
appears with z = 0.6 (test statistic) and p = 0.5485 (p-value). Make sure when you use Draw that no other equations are highlighted in Y = and the plots are turned off. The Type I and Type II errors are as follows: The Type I error is to conclude that the proportion of first-time brides who are younger than their groo... |
43 150. b. What is a success for this problem? Solution 9.18 b. A success is having three cell phones in a household. c. What is the level of significance? Solution 9.18 c. The level of significance is the preset α. Since α is not given, assume that α = 0.05. d. Draw the graph for this problem. Draw the horizontal axi... |
as killed to the total fleas found on Fido. This is sample information. The problem gives a preconceived α = 0.01, for comparison, and a 95 percent confidence interval computation. The poem is clever and humorous, so please enjoy it! Example 9.19 My dog has so many fleas, They do not come off with ease. As for shampoo,... |
more. ⎞ ⎠ 17 42 Use the previous information to sketch a picture of this situation. Clearly label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Figure 9.11 Compare α and the p-value: Indicate the correct decision (reject or do not reject the null hypothesis) and the reason for it,... |
testing a sample mean without a known population standard deviation. Therefore, we need to use a Student's t-distribution. Assume the underlying population is normal. 3. Do the calculations: We will input the sample data into the TI-83 as follows. 546 Chapter 9 | Hypothesis Testing with One Sample Figure 9.13 Figure 9... |
005, we cannot reject the null. Therefore, we conclude that there is not enough evidence to support the claim of higher brain cancer rates for the cell phone users. 9.6 | Hypothesis Testing of a Single Mean and Single Proportion This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 9 |... |
an average of three pairs of jeans. Survey eight people from your class to determine if the average is higher than three. Assume the population is normal. 1. H0: _____________ 2. Ha: _____________ 3. In words, define the random variable. __________ = ______________________ 4. The distribution to use for the test is __... |
of significance is called the preconceived α or the preset α. normal distribution a bell-shaped continuous random variable X, with center at the mean value (μ) and distance from the center to the inflection points of the bell curve given by the standard deviation (σ) We write X ~ N(μ, σ). If the mean value is 0 and th... |
less than, greater than, or not equals symbols, i.e., (≠, >, or <). 3. If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. 4. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probabili... |
deciding whether or not to reject the null the hypothesis, keep these two parameters in mind: 1. α > p-value, reject the null hypothesis. 2. α ≤ p-value, do not reject the null hypothesis. 9.5 Additional Information and Full Hypothesis Test Examples The hypothesis test itself has an established process. This can be su... |
othesis Testing If there is no given preconceived α, then use α = 0.05. Types of Hypothesis Tests • Single population mean, known population variance (or standard deviation): Normal test. • Single population mean, unknown population variance (or standard deviation): Student's t-test. • Single population proportion: Nor... |
with a standard deviation of 1.8 hours. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of homework has increased, what would the null and alternative hypotheses be? The distribution of the population is normal. a.... |
an old sunken ship. Suppose the null hypothesis, H0, is the sunken ship does not contain buried treasure. State the Type I and Type II errors in complete sentences. 19. A microbiologist is testing a water sample for E. coli. Suppose the null hypothesis, H0, is the sample does not contain E. coli. The probability that ... |
np is less than five. What must you do to be able to perform a valid hypothesis test? 31. You are performing a hypothesis test of a single population proportion. The data come from which distribution? 9.4 Rare Events, the Sample, and the Decision and Conclusion 32. When do you reject the null hypothesis? 33. The proba... |
homework each week has increased. Assume This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 9 | Hypothesis Testing with One Sample 557 the distribution of homework times is approximately normal. 41. Is this a test of means or proportions? 42. What symbol represents the random varia... |
0: p = 0.25 and Ha: p ≠ 0.25. Is this a left-tailed, right-tailed, or two-tailed test? 52. Draw the general graph of a left-tailed test. 53. Draw the graph of a two-tailed test. 54. A bottle of water is labeled as containing 16 fluid ounces of water. You believe it is less than that. What type of test would you use? 55... |
. About half of Americans prefer to live away from cities, given the choice. h. Europeans have a mean paid vacation each year of six weeks. i. The chance of developing breast cancer is under 11 percent for women. j. Private universities' mean tuition cost is more than $20,000 per year. 63. A recent survey of 273 random... |
. d. 29 percent of high school students take physical education every day. e. Less than 5 percent of adults ride the bus to work in Los Angeles. f. The mean number of cars a person owns in his or her lifetime is not more than 10. g. About half of Americans prefer to live away from cities, given the choice. h. Europeans... |
than seven hours of sleep per night, on average? The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at least seven when, in fact, the mean number of hours a. b. c. d. is more than seven hours. is at most seven hours. is at least seven hours. is less than seven hour... |
of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population. a. Is this a test of one mean or proportion? b. State the null and alternative hypotheses. H0: ____________________ Ha: ____________________ Is this a right-tailed, left-tailed, ... |
pg or better by 2016. From past studies on fuel economy, it is known that the standard deviation of a typical fleet is 7.6 mpg. An auto manufacturer selects a random sample of 55 cars and light trucks and finds the sample mean fuel economy to be 34.6 mpg with a standard deviation of 10.3 mpg. Can the manufacturer claim... |
, most people don't believe her. You decide to check this out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. Now, what do you think? 81. A Nissan Motor Corporation advertisement read, “The average man’s I.Q. is 107. The averag... |
macaroni and cheese. It's high in taste and low in cost and nutritional value. One day, as I sat down to determine the meaning of life, I got a serious craving for this, oh, so important, food of my life. So I went down the street to Greatway to get a box of macaroni and cheese, but it was SO expensive! $2.02!!! Can y... |
hast seen a ghost! It is but a figment of your imagination! HAMLET: I beg to differ; I know of a certainty that five-and-seventy in one hundred of us, condemned to the whips and scorns of time as we are, have gazed upon a spirit of health, or goblin damn’d, be their intents wicked or charitable. POLONIUS: If thou dost... |
not our test. (Horatio and Polonius leave together.) HAMLET: To reject, or not reject, that is the question: whether ‘tis nobler in the mind to suffer the slings and arrows of outrageous statistics, or to take arms against a sea of data, and, by opposing, end them. (Hamlet resignedly attends to his task.) (Curtain fal... |
sometimes, westernized in naming their children. I have a feeling that, while 70 percent or more of my mother’s generation would have names with “ko” at the end, the proportion has dropped among my peers. I wrote down all my Japanese friends’, ex-classmates’, coworkers’, and acquaintances’ names that I could remember.... |
report they fear public speaking. Conduct a hypothesis test to determine if the percentage at her school is less than 40. 98. Sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty. To test if 68 percent also represents California’s percent for full-time faculty ... |
just 8 percent of them were Harleys. Is there good evidence that the proportion of Harleys among stolen motorcycles is significantly less than their share of all motorcycles? After conducting the test, what decision and conclusion would you make? a. Reject H0: There is sufficient evidence to conclude that the proporti... |
conclude that the mean number of hours is more than 4.75. Hypothesis testing: For the following 10 exercises, answer each question. a. State the null and alternate hypotheses. b. State the p-value. c. State alpha. d. What is your decision? e. Write a conclusion. f. Answer any other questions asked in the problem. This... |
significance. What is the possible proportion of patrons who do borrow books from the Owensboro Library? 111. The Weather Underground reported that the mean amount of summer rainfall for the northeastern United States is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amo... |
standard deviation of 45 minutes. At α = 0.01 level, is the student academic group’s claim correct? REFERENCES 9.1 Null and Alternative Hypotheses Centers for Disease Control and Prevention. (n.d.). Physical activity facts. Retrieved from http://www.cdc.gov/ healthyschools/physicalactivity/facts.htm National Institute... |
. Available at http://files.eric.ed.gov/fulltext/ED530062.pdf Toastmasters detail.asp?CategoryID=1&SubCategoryID=10&ArticleID=429&Page=1 International. Retrieved (n.d.). from http://toastmasters.org/artisan/ U.S. Census Bureau. (n.d.). Language use. Retrieved from https://www.census.gov/topics/population/language-use.h... |
omial distribution 33 The outcome of winning is very unlikely. 35 H0: μ > = 73 Ha: μ < 73 The p-value is almost zero, which means there is sufficient data to conclude that the mean height of high school students who play basketball on the school team is less than 73 inches at the 5 percent level. The data do support th... |
, when it really is at least $100,000. Type II error: We conclude that the mean starting salary is at least $100,000 when, in fact, it is less than $100,000. d. Type I error: We conclude that the proportion of high school seniors who take physical education daily is not 29%, when it really is 29%. Type II error: We con... |
Stax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 9 | Hypothesis Testing with One Sample 575 b. Ha: μ < 50,000 c. Let X ¯ = the average lifespan of a brand of tires. d. normal distribution e. z = -2.315 f. p-value = 0.0103 g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Reject ... |
. Student’s t-distribution e. t = –1.12 f. p-value = 0.300 g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Do not reject the null hypothesis. iii. Reason for decision: The p-value is greater than 0.05. iv. Conclusion: At the 5 percent significance level, there is insufficient evidence to conclude that the ... |
0.0036 g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Reject the null hypothesis. iii. Reason for decision: The p-value is less than 0.05. iv. Conclusion: There is sufficient evidence to conclude that the percentage of Americans who have been diagnosed with the disease is less than 13 percent. i. (0, 0.0... |
to the level of significance, the exact p-value based on binomial probabilities should be calculated whenever possible. This is beyond the scope of this course. 89 a. H0: μ ≥ 22 b. Ha: μ < 22 c. Let X ¯ = the mean number of bubbles per blow. d. Student's t-distribution e. –2.667 f. p-value = 0.00486 g. Check student’s... |
-4s confidence interval is (0.004, 0.144). 95 a. H0: p = 0.50 b. Ha: p < 0.50 c. Let P′ = the proportion of friends that has a pierced ear. d. normal for a single proportion e. –1.70 f. p-value = 0.0448 g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Reject the null hypothesis. iii. Reason for decision: Th... |
2, 0.2070): The plus-4s confidence interval (see chapter 8) is (0.0676, 0.2297). 101 a. H0: μ = 69,110 b. Ha: μ > 69,110 c. Let X ¯ = the mean salary in dollars for California registered nurses. d. Student's t-distribution e. t = 1.719 f. p-value: 0.0466 g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Reje... |
high usage and low usage, respectively. We would need to expand our sample base to include these possibilities if we wanted to generalize this claim to the entire nation. 111 a. H0: µ ≥ 11.52 Ha: µ < 11.52 b. p-value = 0.000002 which is almost 0. c. alpha = 0.05. d. Reject the null hypothesis. e. At the 5 percent sign... |
example, researchers are interested in the effect aspirin has in preventing heart 584 Chapter 10 | Hypothesis Testing with Two Samples attacks. Over the last few years, newspapers and magazines have reported various aspirin studies involving two groups. Typically, one group is given aspirin and the other group is give... |
with unknown and possibly unequal population standard deviations is called the Aspin-Welch t-test. The degrees of freedom formula was developed by Aspin-Welch. The comparison of two population means is very common. A difference between the two samples depends on both the means and the standard deviations. Very differe... |
⎜ ⎠ ⎝ (s2)2 n2 ⎞ ⎟ ⎠ 2 When both sample sizes n1 and n2 are five or larger, the Student’s t approximation is very good. Notice that the sample variances (s1)2 and (s2)2 are not pooled. (If the question comes up, do not pool the variances.) It is not necessary to compute this by hand. A calculator or computer easily co... |
g – x¯ b Make a decision: Since α > p-value, reject H0. This means you reject μg = μb. The means are different. Press STAT. Arrow over to TESTS and press 4:2-SampTTest. Arrow over to Stats and press ENTER. Arrow down and enter 2 for the first sample mean, 0.866 for Sx1, 9 for n1, 3.2 for the second sample mean, 1 for ... |
a student who graduates from College A has taken more math classes, on average. Both populations have a normal distribution. Test at a 1 percent significance level. Answer the following questions: a. Is this a test of two means or two proportions? Solution 10.2 a. two means b. Are the populations standard deviations k... |
face class. Was the professor correct? The randomly selected 30 final exam scores from each group are listed in Table 10.3 and Table 10.4. 67.6 41.2 85.3 55.9 82.4 91.2 73.5 94.1 64.7 64.7 70.6 38.2 61.8 88.2 70.6 58.8 91.2 73.5 82.4 35.5 94.1 88.2 64.7 55.9 88.2 97.1 85.3 61.8 79.4 79.4 Table 10.3 Online Class 77.9 95... |
ENTER. Arrow down to Calculate and press ENTER. NOTE Be careful not to mix up the information for Group 1 and Group 2! 590 Chapter 10 | Hypothesis Testing with Two Samples Solution 10.3 two means a. b. unknown c. Student’s t ¯ d. X ¯ 1 – X 2 e. 1. H0: μ1 = μ2 Null hypothesis: The means of the final exam scores are equ... |
medium, or large? Explain what the size of the effect means for this problem. Solution 10.4 μ1 = 4 s1 = 1.5 n1 = 11 μ2 = 3.5 s2 = 1 n2 = 9 d = 0.384 The effect is small because 0.384 is between Cohen’s value of 0.2 for small effect size and 0.5 for medium effect size. The size of the differences of the means for the t... |
.4 21.5 Table 10.7 West Is there a difference in the weighted alpha of the top 30 stocks of banks in the Northeast and in the West? Test at a 5 percent significance level. Answer the following questions: 592 Chapter 10 | Hypothesis Testing with Two Samples a. Is this a test of two means or two proportions? b. Are the p... |
/col30309/1.8 Chapter 10 | Hypothesis Testing with Two Samples 593 Solution 10.6 This is a test of two independent groups, two population means, population standard deviations known. ¯ Random Variable: X ¯ 1 – X 2 = difference in the mean number of months the competing floor waxes last. H0: μ1 ≤ μ2 Ha: μ1 > μ2 The word... |
? Test at a 5 percent level of significance. Engine Sample Mean Number of RPM Population Standard Deviation 1 2 1,500 1,600 Table 10.9 50 60 Example 10.7 An interested citizen wanted to know if Democratic U.S. senators are older than Republican U.S. senators, on average. On May 26, 2013, the mean age of 30 randomly sel... |
significance, from the sample data, there is not sufficient evidence to conclude that the mean age of Democratic senators is greater than the mean age of the Republican senators. 10.3 | Comparing Two Independent Population Proportions When conducting a hypothesis test that compares two independent population proportio... |
difference in the proportions of adult patients who did not react after 30 minutes to Medication A and to Medication B. H0: pA = pB pA – pB = 0 Ha: pA ≠ pB pA – pB ≠ 0 The words is a difference tell you the test is two-tailed. Distribution for the test: Since this is a test of two binomial population proportions, the ... |
but instead of Calculate do Draw. 10.8 Two types of valves are being tested to determine if there is a difference in pressure tolerances. Fifteen out of a random sample of 100 of Valve A cracked under 4,500 psi. Six out of a random sample of 100 of Valve B cracked under 4,500 psi. Test at a 5 percent level of signific... |
the proportion of girls sending texts is less than the proportion of boys sending texts. Press STAT. Arrow over to TESTS and press 6:2-PropZTest. Arrow down and enter 156 for x1, 2169 for n1, 183 for x2, and 2231 for n2. Arrow down to p1: and arrow to less than p2. Press ENTER. Arrow down to Calculate and press ENTER.... |
for group A: 0.10 Estimated proportion for group B: 0.05 Graph: Figure 10.9 Decision: Since α > p-value, reject the H0. Conclusion: At the 5 percent level of significance, from the sample data, there is sufficient evidence to conclude that a larger proportion of white cell phone owners use Phone B than African America... |
of differences is sufficiently large so that distribution of the sample mean of differences is approximately normal. In a hypothesis test for matched or paired samples, subjects are matched in pairs and differences are calculated. The differences are the data. The population mean for the differences, μd, is then teste... |
the mean difference of the sensory measurements. H0: μd ≥ 0 The null hypothesis is zero or positive, meaning that there is the same or more pain felt after taking the medication. That means the subject shows no improvement. μd is the population mean of the differences. Ha: μd < 0 The alternative hypothesis is negative... |
down to Calculate and press ENTER. The p-value is 0.0094, and the test statistic is –3.04. Do these instructions again except, arrow to Draw instead of Calculate. Press ENTER. 10.11 A study was conducted to investigate how effective a new diet was in lowering cholesterol. Results for the randomly selected subjects are... |
μd ≤ 0, Ha: μd > 0 Graph: 604 Chapter 10 | Hypothesis Testing with Two Samples Figure 10.11 Calculate the p-value: The p-value is 0.2150. Decision: If the level of significance is 5 percent, the decision is not to reject the null hypothesis, because α < p-value. What is the conclusion? At a 5 percent level of signific... |
12 Calculate the p-value: The p-value is 0.0716 (using the data directly). Test statistic = 2.18. p-value = 0.0719 using ⎛ ⎝ x¯ d = 3.71, sd = 4.5 ⎞ ⎠. Decision: Assume α = 0.05. Since α < p-value, do not reject H0. Conclusion: At the 5 percent level of significance, from the sample data, there is not sufficient eviden... |
significance. a. Graph: Figure 10.13 b. Calculate the p value. 7. Do you reject or not reject the null hypothesis? Why? 8. Write a clear conclusion using a complete sentence. 608 Chapter 10 | Hypothesis Testing with Two Samples Decreasing Stocks Survey Randomly pick eight stocks from the newspaper. Using two consecuti... |
. 7. Do you reject or not reject the null hypothesis? Why? 8. Write a clear conclusion using a complete sentence. 610 Chapter 10 | Hypothesis Testing with Two Samples KEY TERMS degrees of freedom (df) the number of objects in a sample that are free to vary pooled proportion estimate of the common value of p1 and p2 sta... |
d = mean of the differences. • Distribution: Student’s t distribution with n – 1 degrees of freedom. • If the number of differences is small (less than 30), the differences must follow a normal distribution. • Two samples are drawn from the same set of objects. • Samples are dependent. This OpenStax book is available ... |
) ⎛ pc(1 − pc) ⎝ 1 n A + 1 nB ⎞ ⎠ x¯ 1 and x¯ 2 are the sample means. Cohen’s d is the measure of effect size: d = 1 − x¯ x¯ s pooled 2 where s pooled = (n1 − 1)s1 2 2 + (n2 − 1)s2 n1 + n2 − 2. 10.2 Two Population Means with Known Standard Deviations Normal distributionμ1 − μ2, ⎣ (σ1)2 n1 + (σ2)2 n2 ⎤ ⎥. ⎦ Generally, µ... |
A study is done to test this. 3. A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without the new treatment. The same windshields are then treated, and the experiment is run again. A hypothesis test is conducted. 4. The known standard deviation in salary ... |
a standard deviation of 1.2. A sample of 12 adults has a mean of 6.9 hours slept and a standard deviation of 0.6. 12. Varsity athletes practice five times a week, on average. 13. A sample of 12 in-state graduate school programs at School A has a mean tuition of $64,000 with a standard deviation of $8,000. At School B,... |
124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. 19. Is this a test of mean... |
Samples the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller. Plant Group Sample Mean Height of Plants (inches) Population Standard Deviation Food No food Table 10.19 16 14 2.5 1.5 36. Is the... |
or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 10 | Hypothesis Testing with Two Samples 615 a hypothesis test to determine if the population percents are the ... |
study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal 616 Cha... |
courses with a standard deviation of 0.8. The females took an average of 4 English courses with a standard deviation of 1.0. Are the means statistically the same? 79. A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys... |
the test in Exercise 10.83, but use Lap 5 data this time. 85. Repeat the test in Exercise 10.83, but this time combine the data from Laps 1 and 5. 86. In two to three complete sentences, explain in detail how you might use Terri Vogel’s data to answer the following question: Does Terri Vogel drive faster in races than... |
is insufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2. d. There is sufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2. 90... |
(When using these tests in a real situation, you must first prove that assumption.) 93. A study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university ... |
and the population standard deviation of games won by the National League was 1.11. Of 19 randomly selected World Series games won by the American League, the mean number of games won was 5.76. The mean number of 17 randomly selected games won by the National League was 5.42. Conduct a hypothesis test. 620 Chapter 10 ... |
the same in the Whitney Exhibit for works from 1900 to 1919 as for works from 1920 ⎞ ⎠ 101. A year was randomly picked from 1985 to the present. In that year, there were 2,051 Hispanic students at Cabrillo College out of a total of 12,328 students. At Lake Tahoe College, there were 321 Hispanic students out of a total... |
invasive West Nile virus is less than the proportion of people in the United States in 2010 who contracted neuroinvasive West Nile virus. d. There is sufficient evidence to conclude that the proportion of people in the United States in 2011 who contracted neuroinvasive West Nile virus is more than the proportion of peo... |
�s entertainment software. Thirty-six educational software titles were randomly picked from a catalog. The mean cost was $31.14 with a standard deviation of $4.69. Thirty-five entertainment software titles were randomly picked from the same catalog. The mean cost was $33.86 with a standard deviation of $10.87. Decide w... |
worked again before getting tired and stopping. Of interest was our mean increase in work time. Though not sure, my brother insisted that it was more than two hours. Using the data in Table 10.29, solve our problem. Work hours with breakfast Work hours without breakfast 8 7 9 5 9 8 10 Table 10.29 10.4 Matched or Paire... |
disease after four years. c. There is sufficient evidence to conclude that the method increases the proportion of patients who develop the disease after four years. d. There is insufficient evidence to conclude that the method reduces the proportion of patients who develop the disease after four years. Use the followi... |
7,310 3,160 3,300 3,320 3,630 Mississippi 1,990 2,080 North Carolina 7,090 7,430 Oklahoma 2,630 2,690 South Carolina 3,570 3,580 Tennessee 4,680 5,070 Texas Virginia Table 10.32 15,050 14,980 6,190 6,280 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 10 | Hypothesis Testing wit... |
chocolate bar is taste-tested on consumers. Of interest is whether the proportion of children who like the new chocolate bar is greater than the proportion of adults who like it. 125. The mean number of English courses taken in a two-year time period by male and female college students is believed to be about the same... |
children based on this experiment. The experiment produced the means and standard deviations shown in Table 10.36. Determine the appropriate test and best distribution to use for that test. Left-handed Right-handed Sample size Sample mean 41 97.5 Sample standard deviation 17.5 41 98.1 19.2 Table 10.36 a. Two independe... |
MMWR, 57(28), 765–768. Retrieved from http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5728a1.htm Federal Bureau of Investigation. (n.d.). Texas Crime Rates 1960–1012. Available at http://www.disastercenter.com/crime/ txcrime.htm Hinduja, S. http://cyberbullying.us/blog/sexting-research-and-gender-differences/ (2013). Sexti... |
7 independent group means, population standard deviations and/or variances unknown 9 two proportions 11 independent group means, population standard deviations and/or variances unknown 13 independent group means, population standard deviations and/or variances unknown 15 two proportions 17 The random variable is the d... |
races in Nevada is statistically higher than that in North Dakota. 630 Chapter 10 | Hypothesis Testing with Two Samples 63 the mean difference of the system failures 65 0.0067 67 With a p-value 0.0067, we can reject the null hypothesis. There is enough evidence to support that the software patch is effective in reduci... |
. X ¯ 1 − X 2 is the difference between the mean times for completing a lap in races and in practices. d. e. t20.32 test statistic: –4.70 f. p-value: 0.0001 g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Reject the null hypothesis. iii. Reason for Decision: p-value < alpha iv. Conclusion: At the 5 percent... |
iv. Conclusion: At the 5 percent significance level, there is sufficient evidence to conclude that the mean cost of auto insurance for teenage boys is greater than that for girls. 96 Subscripts: 1 = non-hybrid sedans, 2 = hybrid sedans a. H0: µ1 ≥ µ2 b. Ha: µ1 < µ2 c. The random variable is the difference in the mean ... |
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