Question

The manager of a supermarket would like the variance of the waiting times of the customers not to exceed 4.0 minutes-squared. She would add a new cash register if the variance exceeds this threshold. She regularly checks the waiting times of the customers to ensure that the variance does not rise above the allowed level. In a recent random sample of 28 customer waiting times, she computes the sample variance as 6.5 minutes-squared. She believes that the waiting times are normally distributed. Use Table 3.

a.

Select the null and the alternative hypotheses to test if the threshold has been crossed.

	H0: σ2 ≤ 4.0; HA: σ2 > 4.0
	H0: σ2 = 4.0; HA: σ2 ≠ 4.0
	H0: σ2 ≥ 4.0; HA: σ2 < 4.0

   

b-1.	Calculate the value of the test statistic. (Round your answer to 2 decimal places.)

Test statistic

b-2.

Approximate the p-value.

	p-value > 0.05
	0.010 < p-value < 0.025
	0.025 < p-value < 0.05
	p-value < 0.01

  

b-3.

Do you reject the null hypothesis at the 5% level?

	No, since the p-value is more than α.
	Yes, since the p-value is less than α.
	No, since the p-value is less than α.
	Yes, since the p-value is more than α.

  

c.	Calculate the critical value at the 1% significance level. (Round your answer to 3 decimal places.)

  

Critical value

  

d.

Is action required from the manager?

	Yes, since the value of the test statistic is less than the critical value.
	No, since the value of the test statistic is more than the critical value.
	No, since the value of the test statistic is less than the critical value.
	Yes, since the value of the test statistic is more than the critical value.

Answer 1

The statistical software output for this problem is:

Hence,

a) Hypotheses: Option A is correct.

b - 1) Test statistic = 43.88

b - 2) 0.010 < p-value < 0.025

b - 3) Yes, since the p-value is less than α.

c) Critical value = 40.113

d) Yes, since the value of the test statistic is more than the critical value.