Question

The day after Thanksgiving is known as "Black Friday" as retailers open early on Friday morning, or sometimes late at night on Thanksgiving Day itself, to start the holiday shopping season. However, there is a current social movement afoot to allow employees to enjoy the Thanksgiving holiday by discouraging consumers from patronizing stores that open on Thanksgiving Day evening. SaMart believes that consumers will not follow the social pressure and will continue to show up in large numbers at midnight on Thanksgiving Day to start "Black Friday." Consider the following hypothesis test that measures the average number of customers waiting outside all SaMart locations to start "Black Friday": H0: ? ? 202 customers usually show up early on Black Friday HA: ? < 202 customers will show up (i.e. fewer) if the "social movement" occurs It's now Black Friday. At our 85 SaMart stores, there are an average of 188 customers waiting for those SaMart stores to open early. The population standard deviation is known to be 17. Use Table 1. We are going to test whether customers continue to show up early on Black Friday, or whether the "social movement" has resulted in a statistically observed change in customer behavior for SaMart.

a. What is the critical value for the test with ? : 0.10 and with ?-O your answers to 2 decimal places.) 5? Negative values should be indicated b, minus si Round Critical Value a-0.10 ?-0.05 b. Calculate the value of the test statistic. (If there is a negative value, it should be indicated by a minus sign. Round your answer to 2 decimal places.) NOTE: the next automated question will ask you the p-value that corresponds to this test statistic. Be prepared to provide that numerical answer. Test statistic c. Does the above sample evidence enable us to reject the null hypothesis at a-0.10 Yes since the value of the test statistic is less than the negative critical value No since the value of the test statistic is not less than the negative critical value Yes since the value of the test statistic is not less than the negative critical value. No since the value of the test statistic is less than the negative critical value. 05 Does the above sam ple evidence enable us to reject the null hypothesis at ? you to provide a short answer to this question: At the level of a in part d. of this problem, what's the practical implication of this hypothesis test; that is, what does it mean to SaMart and opening late-night for Black Friday? NOTE: he next automated question will also ask d. Yes since the value of the test statistic is less than the negative critical value No since the value of the test statistic is not less than the negative critical value. Yes since the value of the test statistic is not less than the negative critical value No since the value of the test statistic is less than the negative critical value.

Following up on the Black Friday question. Now provide these answers:

What was the p-value that corresponds to your test statistic?; and,

At the level of ? in part d. of the previous problem, what's the practical implication of this hypothesis test; that is, what does it mean to SaMart and opening late-night for Black Friday? (Write a short answer showing me you know what it means to accept or reject the null hypothesis in this SaMart question.)

Answer 1

a) At alpha = 0.10, the critical values are z^* = -1.28

   At alpha = 0.05, the critical values are z^* = -1.645

b) The test statistic z = ( $\bar x - \mu$ )/( $\sigma/\sqrt n$ )

                                 = (188 - 202)/(17/sqrt(85))

                                 = -7.59

c) At alpha = 0.10, as the test statistic value is less than the critical value (-7.59 < -1.28), so we should reject H₀.

Opyion - A is correct.

d) At alpha = 0.05, as the test statistic value is less than the critical value (-7.59 < -1.645), so we should reject H₀.

Option - A is correct.

P-value = P(Z < -7.59)

             = 0

At alpha = 0.05, as the P-value is less than the significance level (0 < 0.05), we should reject H₀.