Question

A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.75 inches. The population standard deviation is assumed to be 0.15 inches. At α=0.05, should the business reject the supplier’s claim?

Yes, since p<α, we reject the null and the null is the claim

No, since p>α, we fail to reject the null and the null is the claim

No, since p>α, we reject the null and the null is the claim

Yes, since p>α, we fail to reject the null and the null is the claim

The company’s cleaning service states that they spend more than 46 minutes each time the cleaning service is there. The company times the length of 37 randomly selected cleaning visits and finds the average is 46.5 minutes. Assuming a population standard deviation of 5.2 minutes, can the company support the cleaning service’s claim at α=0.10?

No, since p>α, we fail to reject the null. The claim is the alternative, so the claim is not supported

Yes, since p<α, we reject the null. The claim is the null, so the claim is not supported

Yes, since p<α, we fail to reject the null. The claim is the null, so the claim is not supported

No, since p<α, we reject the null. The claim is the alternative, so the claim is supported

A customer service phone line claims that the wait times before a call is answered by a service representative is less than 3.3 minutes. In a random sample of 62 calls, the average wait time before a representative answers is 3.24 minutes. The population standard deviation is assumed to be 0.29 minutes. Can the claim be supported at α=0.08?

No, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is not supported

No, since test statistic is in the rejection region defined by the critical value, fail to reject the null. The claim is the alternative, so the claim is not supported

Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported

Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported

A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 28 residents in that town has a mean credit card debt of $3590 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported, assuming this is a normally distributed data set?

No, since p of 0.12 is greater than 0.10, reject the null. Claim is null, so is not supported

Yes, since p-value of 0.12 is less than 0.55, reject the null. Claim is alternative, so is supported

Yes, since p-value of 0.12 is greater than 0.10, fail to reject the null. Claim is null, so is supported

No, since p-value of 0.12 is greater than 0.10, fail to reject the null. Claim is alternative, so is not supported

Answer 1

1)

Hypothesis:
H0 : mu = 26.7
Ha :mu not equals to 26.7

test statistics:

z = (x -mean)/(s/sqrt(n))
= ( 26.75 - 26.7)/(0.15/sqrt(48))
= 2.3094

p value = .0209
Yes, since p<α, we reject the null and the null is the claim

2)

Hypothesis:
H0 : mu = 46
Ha :mu > 46

test statistics:

z = (x -mean)/(s/sqrt(n))
= ( 46.5 - 46)/(5.2/sqrt(37))
= 0.5849

p value =   .2793

No, since p>α, we fail to reject the null. The claim is the alternative, so the claim is not supported