Question

Given the scenario below, what is the obtained statistic (obtained value)? Americans typically take off 5 sick days each year, with a standard deviation of 2 days. A researcher would like to know whether psychiatrists take off less sick days than the average American. The researcher obtains a sample of 16 psychiatrists who, on average, take 3 days of sick leave a year. Test this researcher s hypothesis using an alpha level of 01.

Answer 1

The provided sample mean is X = 3 and the known population standard deviation is o = 2, and the sample size is n = 16. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: 4 = 5 Ha: u <5 This corresponds to a left-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 left-tailed test is ze = -2.33. The rejection region for this left-tailed testis R = {z: z < -2.33} (3) Test Statistics The Z-statistic is computed as follows: z = X - MO on 3 - 5 2/ 16 = -4 (4) Decision about the null hypothesis -2.33, it is then concluded that Since it is observed that z = -4 < ze = the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0, and since p = 0 <0.01, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean u is less than 5, at the 0.01 significance level. Confidence Interval The 99% confidence interval is 1.712 < u < 4.288.

Obtained value = -4

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