Hypothesis testing on samples with fewer than 30 participants can be carried out by using the t-value for the corresponding level of significance in place of the z value when setting up the decision rule.

A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are below. Using a 5% significance level, test the hypothesis that the three mean commuting mileages are the same. (Let 1 = Working-class, 2 = Professional (middle incomes), and 3 = Professional (wealthy).) Part (a) Part (b) Part (c) Part (d) Part (e) Part (f) Working-class 18.1 27.5 49.7 10.1 65.8 47.2 20.1 51.8 Professional (middle incomes) 17.0 17.5 22.7 7.6 10.2 2.9 7.3 14.5 What is the test statistic? (Round your answer to two decimal places.) Part (g) What is the p-value? (Round your answer to four decimal places.) Professional (wealthy) 9.1 7.2 4.9 12.8 11.6 29.0 16.3 9.5

The manufacturer of a new eye cream claims that the cream reduces the appearance of fine lines and wrinkles after just 14 days of application. To test the claim, 10 women are randomly selected to participate in a study. The number of fine lines and wrinkles that are visible around each participant’s eyes is recorded before and after the 14 days of treatment. The following table displays the results. Test the claim at the 0.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let women before the treatment be Population 1 and let women after the treatment be Population 2. Number of Fine Lines and WrinklesBefore    11    14    13    12    15    14    9    11    11    14After    10    14    11    13    13    13    8    12    10    15 Step 1 of 3 :  State the n ull and alternative hypotheses for the test. Fill in the blank below. H0Ha: μd=0: μd⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0     3) draw a conclusion and form a decision (word it like "we…

The manufacturer of a new eye cream claims that the cream reduces the appearance of fine lines and wrinkles after just 14 days of application. To test the claim, 10 women are randomly selected to participate in a study. The number of fine lines and wrinkles that are visible around each participant's eyes is recorded before and after the 14 days of treatment. The following table displays the results. Test the claim at the 0.02 level of significance assuming that the population distribution of the paired differences is approximately normal. Let women before the treatment be Population 1 and let women after the treatment be Population 2. Number of Fine Lines and Wrinkles Before 12 14 13 11 11 15 10 10 10 9 After 10 14 12 12 12 15 9 7 8 Copy Data Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.

A machine in a factory must be repaired if it produces more than 10% defectives in a day.  A random sample of 100 produced items contains 15 defectives, and the supervisor says that the machine must be repaired. The P-value for the appropriate statistical test to evaluate the supervisor's decision is closest to:

hterested in comparing the amount of time spent watching commercials by female students as compared to male students. Independent simple random samples of 14 female students and 17 male students were selected, and each student was asked how many hours they had watched television commercials during the previous week. The summary statistics are listed in the table below. Is there compelling statistical evidence that the mean amount of time spent watching commercials is lower for female students than it is for male students? Use a significance value of 0.05. Two-Sample T-Test Mean time Standard Deviation time Sample IN spent watching spent watching commercials commercials Female 14 11.4 4.1 Male 17 16.8 4.7 Null Hypothesis, HO Alternative Hypothesis, H1 Test Statistic, t Pavalue Significance levelt Conclusion

To determine whether car ownership affects a student's academic achievement, two random samples of 100 male students were each drawn from the student body. The grade point average for the n₁ = 100 nonowners of cars had an average and variance equal to ₁ 2.70 and s= .36, while ₂ 2.54 and s .40 for the n₂ 100 car owners. Do the data present sufficient evidence to indicate a difference in the mean achievements between car owners and nonowners of cars? Test using a = .05. P -

In a survey, 45% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result to be too high, so he randomly selected 240 pet owners and discovered that 104 of them spoke to their pet on the telephone. Does the veterinarian have a right to be skeptical? Use the a = 0.01 level of significance. Because npo (1- Po) = 59.4 > 10, the sample size is less than 5% of the population size, and the sample is given to be random, the requirements for testing the hypothesis satisfied. are (Round to one decimal place as needed.) What are the null and alternative hypotheses? 0.45 versus H,: P Hо: р (Type integers or decimals. Do not round.) 0.45 Find the test statistic, zo. Zo = (Round to two decimal places as needed.)

In a previous poll, 46% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 515 of 1172 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the a= 0.05 significance level. Because npo (1- Po) = V 10 and the sample size is V 5% of the population size, and the sample v the requirements for testing the hypothesis v satisfied. (Round to one decimal place as needed.) What are the null and alternative hypotheses? Ho: versus H, (Type integers or decimals. Do not round.) Find the test statistic, Zo- Zo (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) Is there sufficient evidence that the proportion of families with children…

In a survey, 36% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result to be too high, so he randomly selected 240 pet owners and discovered that 85 of them spoke to their pet on the telephone. Does the veterinarian have a right to be skeptical? Use the x = 0.1 level of significance. Because npo (1-P) = 55.3 > 10, the sample size is (Round to one decimal place as needed.) What are the null and alternative hypotheses? Ho: versus H₁: (Type integers or decimals. Do not round.) less than 5% of the population size, and the sample is given to be random, the requirements for testing the hypothesis are satisfied.