Question

On average, Americans have lived in 3 places by the time they are 18 years old. Is this average more for college students? The 44 randomly selected college students who answered the survey question had lived an average of 3.15 places by the time they were 18 years old. The standard deviation for the survey group was 0.9. What can be concluded at the a = 0.01 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? Select an answer H: Select an answer c. The test statistic ? (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is a f. Based on this, we should Select an answer the null hypothesis. g. Thus, the final conclusion is that ... The data suggest that the populaton mean is significantly more than 3 at a = 0.01, so there is statistically significant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is more than 3. The data suggest that the sample mean is not significantly more than 3 at a = 0.01, so there is statistically insignificant evidence to conclude that the sample mean number of places that college students lived in by the time they were 18 years old is more than 3.15. The data suggest that the population mean is not significantly more than 3 at -0.01. so there is statistically insignificant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is more than 3. h. Interpret the p value in the context of the study. There is a 13.75361716% chance that the population mean number of places that college students lived in by the time they were 18 years old is greater than 3 If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 44 college students then there would be a 13.75361716% chance that the population mean number of places that these college students lived in by the time they were 18 years old would be greater than 3 Bi ch

Answer 1

The provided sample mean is X = 3.15 and the known population standard deviation is o = 0.9, and the sample size is n = 44. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: р = 3 Ha: u > 3 This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.01, and the critical value for a right-tailed test is ze = 2.33. The rejection region for this right-tailed test is R= 2.33} (3) Test Statistics The z-statistic is computed as follows: 2 = I - po o/n 3.15 3 0.9/144 1.106 (4) Decision about the null hypothesis Since it is observed that z = 1.106 < zc = 2.33, it is then concluded that the null hypothesis is not rejected. 0.1345 > Using the P-value approach: The p-value is p = 0.1345, and since p 0.01, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean j is greater than 3, at the 0.01 significance level. Confidence Interval The 99% confidence interval is 2.801 < u < 3.499. Graphically. Z-Test Results: t-stats = 1.106, p-value =0.1345 0.40 0.35 0.30- 0.25 0.20 - 0.15 - 0.10 - 0.05 0.00 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

g) last option ( third) is correct.

h) option first.

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