Question

It seems these days that college graduates who are employed full-time work more than 40-hour weeks. Data are available that can help us decide if this is true. A survey was recently sent to a group of adults selected at random. There were 15 respondents who were college graduates employed full-time. The mean number of hours worked per week by these 15 respondents was 45 hours, with a standard deviation of 9 hours. Assume that the population of hours worked per week by college graduates employed full-time is normally distributed with mean jl. Can we conclude that is greater than 40 hours? Use the 0.05 level of significance. Perform a one-tailed test. Then fill in the table below Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

Answer 1

45 and the sample standard deviation is s = 9 The provided sample mean is X and the sample size is n = 15. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: ji s 40 Ha: ji > 40 This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region 0.05, and the Based on the information provided, the significance level is a critical value for a right-tailed test is tc = 1.761. The rejection region for this right-tailed test is R=t:t > 1.761 (3) Test Statistics The t-statistic is computed as follows: - MO t Ž s/n 45 – 40 9/15 2.152 (4) Decision about the null hypothesis Since it is observed that t = 2.152 >te = 1.761, it is then concluded that the null hypothesis is rejected. = -0.0247 < Using the P-value approach: The p-value is p = 0.0247, and since p 0.05, 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 greater than 40, at the 0.05 significance level.

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