Review Exercises 471 random sample of 150 households in the city, and finds that the sample mean number of people is 2.3 with a sample standard deviation of 1.5. Can you conclude that the mean number of people per household is less than 2.5? a. State the null and alternate hypotheses. H0 : �� = 2.5, H1: �� < 2.5 b. Should we perform a z-test or a t-test? Explain. t-test c. Compute the value of the test statistic. −1.633 d. Do you reject H0? Use the �� = 0.01 level. No e. State a conclusion. 8. Job satisfaction: In 2012, the General Social Survey sampled 762 employed people and asked them how satisfied they were with their jobs. Of the 762 people sampled, 386 said that they were completely satisfied or very satisfied with their jobs. Can you conclude that more than 45% of employed people in the United States are completely or very satisfied with their jobs? a. State the null and alternate hypotheses. H0 : p = 0.45, H1: p > 0.45 b. Compute the value of the test statistic. 3.14 c. Do you reject H0? Use the �� = 0.01 level. Yes d. State a conclusion. 9. Sugar content: The sugar content in milligrams of a syrup used to pack canned fruit is measured for 8 batches of syrup. The measurements are normally distributed, and the sample standard deviation is s = 3. Can you conclude that the population standard deviation is greater than 2? Use the �� = 0.01 level of significance. No, do not reject H0. 10. Interpret computer output: The following output from MINITAB presents the results of a hypothesis test. �������� ���� ���� = �� �� ���� ������ = �� �� ������ �������������� ���������������� ������������������ = �� �� �� �� ������ �� �� ������ �� �������� ���� �������� ���� �������� �� �������� ����~ ���� .�� ������, �� ������/ a. What are the null and alternate hypotheses? H0 : �� = 4.7, H1: �� ≠ 4.7 b. What is the value of the test statistic? 2.074 c. What is the P-value? 0.038 d. Do you reject H0 at the �� = 0.05 level? Yes e. Do you reject H0 at the �� = 0.01 level? No 11. Interpret calculator display: The following TI-84 Plus display presents the results of a hypothesis test. a. Is this a test for a mean, a proportion, or a standard deviation? Proportion b. What are the null and alternate hypotheses? H0 : p = 0.2, H1: p < 0.2 c. What is the value of the test statistic? −2.25 d. What is the P-value? 0.0122244334 e. Do you reject H0 at the �� = 0.05 level? Yes f. Do you reject H0 at the �� = 0.01 level? No 12. How many TV sets? A survey organization sampled 60 households in a community and found that the sample mean number of TV sets per household was 3.1. The population standard deviation is �� = 1.5. Can you conclude that the mean number of TV sets per household is greater than 3? a. State the null and alternate hypotheses. H0 : �� = 3, H1: �� > 3 b. Should we perform a z-test or a t-test? Explain. z-test c. Compute the value of the test statistic. 0.52 d. Do you reject H0? Use the �� = 0.01 level. No e. State a conclusion. 13. Crackers: Boxes of crackers are filled by a machine. The weights of a random sample of 25 boxes of crackers have standard deviation s = 5 grams. Assume the weights are normally distributed. Can you conclude that the population standard deviation is less than 10 grams? Use the �� = 0.05 level of significance. Yes, reject H0. 14. How much rent? A housing official in a certain city claims that the mean monthly rent for apartments in the city is more than $1000. To verify this claim, a simple random sample of 40 renters in the city was taken, and the sample mean rent paid was $1100 with a sample standard deviation of $300. Can you conclude that the mean monthly rent in the city is greater than $1000?
navidi_monk_elementary_statistics_2e_ch7-9
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