Section 9.3 Hypothesis Tests for a Population Mean, Standard Deviation Unknown 439 Performing hypothesis tests with technology The following output (from MINITAB) presents the results of Example 9.17. �������� ���� ���� = �� �� ���� ������ = �� �� �� *�� ���� �� �� ������ �� �������� �� ���������� ���������� �� �������� ���� �������� �� �������� ����~ ���� .�� ��������, �� ��������/ Most of the output is straightforward. The first line specifies the null and alternate hypotheses. The sample size, sample mean, and sample standard deviation are given as ‘‘N,’’ ‘‘Mean,’’ and ‘‘StDev,’’ respectively. The √ quantity labeled ‘‘SE Mean’’ is the standard error of the mean, which is the quantity s∕ n that appears in the denominator of the t statistic. Next, MINITAB provides a 99% confidence interval for ��. Finally, the value of the t statistic and the P-value are given. The following TI-84 Plus display presents the results of Example 9.17. This display was also shown in the solution to Example 9.17. The first line states the alternate hypothesis. The quantity labeled ‘‘Sx’’ is the sample standard deviation s. Step-by-step instructions for performing hypothesis tests with technology are given in the Using Technology section on page 442. Check Your Understanding 3. In Example 9.17, the alternate hypothesis was H1: �� ≠ 3.5 and the P-value for the two-tailed test was P = 0.0256. What would the P-value be for the alternate hypothesis H1: �� < 3.5? 0.0128 4. The following TI-84 Plus display presents the results of a t-test. a. What are the null and alternate hypotheses? H0 : �� = 7, H1: �� < 7 b. What is the sample size? 6 c. How many degrees of freedom are there? 5 d. What is the value of ̄x? 6.68 e. What is the value of s? 0.205 f. What is the value of the test statistic? −3.823593745 g. What is the P-value? 0.00616394 h. Do you reject H0 at the �� = 0.01 level? Yes 5. Refer to the display in Exercise 4. If the sample mean were 6.80 instead of 6.68, what would the P-value be? If you use Table A.3, you may specify that P is between two values. 0.0312 Answers are on page 447.
navidi_monk_elementary_statistics_2e_ch7-9
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