Question

The waiting time to check out of a supermarket has had a population mean of 11.83 minutes.? Recently, in an effort to reduce the waiting? time, the supermarket has experimented with a system in which there is a single waiting line with multiple checkout servers. A sample of 100 customers was? selected, and their mean waiting time to check out was 11.21 minutes with a sample standard deviation of 5.7 minutes. Complete parts? (a) through? (d). Click here to view page 1 of the critical values for the t Distribution. LOADING... Click here to view page 2 of the critical values for the t Distribution. LOADING... a. At the 0.05 level of? significance, using the critical value approach to hypothesis? testing, is there evidence that the population mean waiting time to check out is less than 11.83 ?minutes? What are the null and alternative hypotheses for this? test? A. Upper H 0?: mugreater than11.83 Upper H 1?: muless than or equals11.83 B. Upper H 0?: muless than or equals11.21 Upper H 1?: mugreater than11.21 C. Upper H 0?: muless than11.21 Upper H 1?: mugreater than or equals11.21 D. Upper H 0?: mugreater than or equals11.21 Upper H 1?: muless than11.21 E. Upper H 0?: mugreater than or equals11.83 Upper H 1?: muless than11.83 F. Upper H 0?: muless than or equals11.83 Upper H 1?: mugreater than11.83 What is the test statistic for this? test? nothing ?(Round to four decimal places as? needed.) What is the critical value for this? test? nothing ?(Round to four decimal places as? needed.) What is the conclusion for this? test? Since the test statistic is ? less greater than the critical? value, ? reject do not reject Upper H 0 . There is ? insufficient sufficient evidence to conclude that the population mean waiting time to check out is less than 11.83 minutes. b. At the 0.05 level of? significance, using the? p-value approach to hypothesis? testing, is there evidence that the population mean waiting time to check out is less than 11.83 ?minutes? What is the? p-value for this? test? nothing ?(Round to four decimal places as? needed.) ?? What is the conclusion for this? test? Since the? p-value is ? greater less than alpha?, ? reject do not reject Upper H 0 . There is ? sufficient insufficient evidence to conclude that the population mean waiting time to check out is less than 11.83 minutes. c. Interpret the meaning of the? p-value in this problem. Choose the correct answer below. A. The? p-value is the probability of obtaining a sample whose mean is 11.21 minutes or? less, assuming the population mean is less than 11.83 minutes. B. The? p-value is the probability of obtaining a sample whose mean is 11.21 minutes or? greater, assuming the population mean is greater than or equal to 11.83 minutes. C. The? p-value is the probability of obtaining a sample whose mean is 11.21 minutes or? less, assuming the population mean is greater than or equal to 11.83 minutes. d. Compare your conclusions in? (a) and? (b). Which of the following statements best describes the relationship between the conclusions in? (a) and? (b)? A. The conclusions are unrelated. B. The conclusions are the? same, by sheer coincidence. C. The conclusions are different because the critical value approach and the? p-value approach are two fundamentally different statistical methods. D. The conclusions are the same because the critical value approach and the? p-value approach are mathematically identical.

Answer 1

here =11.83, =11.21, n=100

(first part)a. At the 0.05 level of? significance, using the critical value approach to hypothesis? testing, is there evidence that the population mean waiting time to check out is less than 11.83 ?minutes?

right choice is D. H0?: 11.83 and H1: <11.83

(second part) What is the test statistic for this? test?

the test statistic t=(-)/(s/sqrt(n))=(11.21-11.83)/(5.7/sqrt(100))=1.0877 with n-1=100-1=99 df

nothing ?(Round to four decimal places as? needed.)

(third part) What is the critical value for this? test? nothing ?(Round to four decimal places as? needed.)

one-tailed critical t(0.05,99)=1.6604

(fouth part) What is the conclusion for this? test?

Since the test statistic is lessthan the critical? value, do not reject Upper H 0 . There is insufficient sufficient evidence to conclude that the population mean waiting time to check out is less than 11.83 minutes.

(fifth part) b. At the 0.05 level of? significance, using the? p-value approach to hypothesis? testing,

What is the? p-value for this? test? nothing ?(Round to four decimal places as? needed.)

p-value=0.1397?

? What is the conclusion for this? test? Since the? p-value is greater than alpha?, do not reject Upper H 0 . There is insufficient evidence to conclude that the population mean waiting time to check out is less than 11.83 minutes.

c. Interpret the meaning of the? p-value in this problem.

right choice is C. The? p-value is the probability of obtaining a sample whose mean is 11.21 minutes or? less, assuming the population mean is greater than or equal to 11.83 minutes.

d. Compare your conclusions in? (a) and? (b).

D. The conclusions are the same because the critical value approach and the? p-value approach are mathematically identical.