Question

10. The established mean for the number of copies a customer makes per visit at a copy store is 37.   A store employee claims the actual number of copies made per visit is less.    A sample of 70 customers was taken and showed an average of 32 copies per customer. The population standard deviation is known to be 25 copies. At alpha = 0.10, test the employee's claim. For question #10 (answer goes directly below), select the alternative hypothesis from choices given. For question #11, enter your calculated z-value.  For question #12, convert your answer from #11 to a  P-Value and place it in the space provided. For question #13, answer True or False as to the rejection of the null hypothesis.

10. Select your answer for the alternative hypothesis from choices given (see directly below to enter your answer for #10).

11. Enter your calculated z-value

12.  Enter your  P-Value (converted from your answer on #11), given to the ten thousandths place

13. True or False: The null hypothesis will be rejected.

Answer 1

The provided sample mean is X = 32 and the known population standard deviation is o = 25, and the sample size is n = 70. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: u = 37 Ha: u <37 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 = 0.10, and the critical value for a left-tailed test is %c = -1.28. The rejection region for this left-tailed testis R= {z: z < -1.28} (3) Test Statistics The Z-statistic is computed as follows: X - μo z = 32 - 37 25/70 1.673 g/n (4) Decision about the null hypothesis 1.28, it is then concluded Since it is observed that z = -1.673 < ze = that the null hypothesis is rejected. Using the P-value approach: The p-value is p= 0.0471, and since p = 0.0471 <0.10, 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 37, at the 0.10 significance level. Confidence Interval The 90% confidence interval is 27.085 <u < 36.915.

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