14. A marketing researcher wants to estimate the mean savings (5) realized by shoppers who showroom. Showrooming is the practice of inspecting products in retail stores and then purchasing the products online at a lower price. A random sample of 130 shoppers who recently p a consumer electronics item online after making a visit to a retail store yielded a mean savings of $58 and a standard deviation of $56. The researcher believes the actual mean savings is $47, Complete parts (a) and (b) below. a. Is there evidence that the population mean savings for all showroomers who purchased a consumer electronics item is different from $47? (Use a 0.10 level of significance ) State the null and alternative hypotheses. Ho: u (1) H, : 1 (2) (Type integers or decimals. Do not round. Do not include the $ symbol in your answer.) Identify the critical value(s) The critical value(s) is(are) (Type an integer or a decimal. Round to two decimal places as needed. Use a comma to separate answers as needed.) Determine the test statistic. The test statistic, ISTAT, is (Type an integer or a decimal. Round to two decimal places as needed.) State the conclusion. (3) Ho. There is (4) evidence to conclude that the population mean savings for all showroomers who purchased a consumer electronics item is different from $47. b. Determine the p-value and interpret its meaning. The p-value is (Type an integer or a decimal. Round to three decimal places as needed.) Interpret the meaning of the p-value. Select the correct answer below. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than $11 above $47 if the null hypothesis is false. The p-value is the probability of not rejecting the null hypothesis when it is false. POOOO The p-value is the probability of obtaining a sample mean that is equal to or more extreme than $11 below $47 if the null hypothesis is false. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than $11 away from $47 if the null hypothesis is true. (1) (2) (3) (4) Do not reject sufficient 12 Reject insufficient