Question

11. In one year, an online travel agency reported that summer travelers booked their airline reservations an average of 71.1 days in advance. A random sample of 40 summer travelers in a later year was selected, and the number of days travelers booked their airline reservations in advance was recorded. The data are shown in the accompanying table. Complete parts a and b below. Click the icon to view the data table. a. Perform a hypothesis test using a = 0.05 to determine if the average number of days reservations are booked in advance has changed between the years. Determine the null and alternative hypotheses. Choose the correct answer below. O A. Ho: u#71.1 and Hy: J = 71.1 O B. Ho: 1271.1 and Hy: <71.1 O C. Ho: h = 71.1 and Hy: u#71.1 OD. Ho: 1 = 71.1 and Hu> 71.1 Determine the test statistic, t. (Round to two decimal places as needed.) Determine the critical value(s). The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.) What conclusion should be drawn? Choose the correct answer below. O A. Do not reject the null hypothesis. The data provide sufficient evidence to conclude that the average number of days has changed between the years. O B. Do not reject the null hypothesis. The data do not provide sufficient evidence to conclude that the average number of days has changed between the years. O C. Reject the null hypothesis. The data provide sufficient evidence to conclude that the average number of days has changed between the years. OD. Reject the null hypothesis. The data do not provide sufficient evidence to conclude that the average number of days has changed between the years. b. Use technology to determine the p-value for this test. P-value = (Round to three decimal places as needed.) O 1: Data Table 71 80 95 77 88 59 73 76 88 5571 54 82 76 63 64 69 85 66 77 68 66 92 80 72 86 55 81 74 78 85 59 75 98 73 72 71 76 68 73

Hypothesis Tests for Means

Answer 1

The statistical software output for this problem is:

One sample T hypothesis test: Mean of variable H = 71.7 H = 71.7 Hypothesis test results: Variable Sample Mean Std. Err. DF T-Stat P-value Data 74.275 1.6801967 39 1.5325587 0.1335

From above output:

a) Hypotheses: Option C is correct.

Test statistic = 1.53

Critical values = -2.023, 2.023

Conclusion: Option B is correct.

b) p - Value = 0.134