Question

11.A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random sample of 61 of these screens has a mean life of 2.5 years. The population is normally distributed with a population standard deviation of 0.88 years. At α=0.02, what type of test is this and can you support the organization’s claim using the test statistic?

Claim is alternative, reject the null and support claim as test statistic (-2.66) is in the rejection region defined by the the critical value (-2.05)

Claim is alternative, fail to reject the null and cannot support claim as test statistic (-2.66) is in the rejection region defined by the critical value (-2.05)

Claim is null, reject the null and support claim as test statistic (-2.66) is in the rejection region defined by the critical value (-2.05)

Claim is null, fail to reject the null and cannot support claim as test statistic (-2.66) is in the rejection region defined by the critical value (-2.05)

12. A pharmaceutical company claims that the average cold lasts an average of 8.4 days. They are using this as a basis to test new medicines designed to shorten the length of colds. A random sample of 106 people with colds, finds that on average their colds last 8.28 days. The population is normally distributed with a standard deviation of 0.9 days. At α=0.02, what type of test is this and can you support the company’s claim using the p-value?

Claim is null, reject the null and cannot support claim as the p-value (0.170) is less than alpha (0.02)

Claim is null, fail to reject the null and support claim as the p-value (0.170) is greater than alpha (0.02)

Claim is alternative, fail to reject the null and support claim as the p-value (0.085) is less than alpha (0.02)

Claim is alternative, reject the null and cannot support claim as the p-value (0.085) is greater than alpha (0.02)

13. 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 26.77 inches. The population standard deviation is assumed to be 0.20 inches. At α=0.05, should the business reject the supplier’s claim?

No, 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

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

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

14. 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 47.2 minutes. Assuming a population standard deviation of 5.2 minutes, can the company support the cleaning service’s claim at α=0.10?

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 fail to reject the null. The claim is the alternative, so the claim is not supported

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

15.. 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 3.26 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 not in the rejection region defined by the critical value, 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

No, since test statistic is not 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

Answer 1

11. Let be the mean life of the cheapest screens.

To test: H₀: Vs H_a: To test whether the hypothesized mean (2.8 years) differs significantly from the sample mean (2.5 years), the appropriate test statistic is given by,

Here, = sample mean = 2.5    = Population standard deviation = 0.88 and n = sample size =61 Substituting these values in the formula for test statistic,

Comparing the test statistic with the critical value obtained from tnormal tables for level, , the critical region is given by CR = Z < . Here Z = -2.66 < -2.05, hence there is not sufficient evidence to support the null hypothesis. Hence, H₀ may be rejected at 2% level of significance. Hence, Claim is alternative, reject the null and support claim as test statistic (-2.66) is in the rejection region defined by the the critical value (-2.05).

12.

Let be the mean days suffered from cold.

To test: H₀: Vs H_a: To test whether the hypothesized mean (8.4 days) differs significantly from the sample mean (8.28 days), the appropriate test statistic is given by,

Here, = sample mean = 8.28 = Population standard deviation = 0.9 and n = sample size =106 Substituting these values in the formula for test statistic,

Since the p value obtained for the test 0.170 > 0.02, we have sufficient evidence to support the null hypothesis.Thus, H₀ may be accepted at 0.02 level of significance.

Hence, here, the claim is null, fail to reject the null and support claim as the p-value (0.170) is greater than alpha (0.02).

13.

Let be the average length of copper tubings.

To test: H₀: Vs H_a: To test whether the hypothesized mean (26.70) differs significantly from the sample mean (26.77), the appropriate test statistic is given by,

Here, = sample mean = 26.70 = Population standard deviation = 0.2 and n = sample size =48 Substituting these values in the formula for test statistic,

Here, the test statistic value 2.425 is greater than the tabled value for α = 0.05, Z = 1.96.Hence it lies in the rejection region.

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

14.

Let be the average time spend on cleaning.

To test: H₀: Vs H_a: To test whether the hypothesized mean (46) differs significantly from the sample mean (47.2), the appropriate test statistic is given by,

Here, = sample mean = 47.2    = Population standard deviation = 5.2 and n = sample size =37 Substituting these values in the formula for test statistic,

The critical value corresponding to 1 - alpha = 0.9, (area to the right of the curve) is given by:

Here, the test statistic value 1.4 is greater than the tabled value for α = 0.10, Z = 1.28. Hence it lies in the rejection region.

The correct option would be:

Since p<α, we reject the null. The claim is the alternative, so the claim is supported.

15.

Let be the average wait time.

To test: H₀: Vs H_a: To test whether the hypothesized mean (3.3) differs significantly from the sample mean (3.26), the appropriate test statistic is given by,

Here, = sample mean = 3.26    = Population standard deviation = 0.29 and n = sample size =62 Substituting these values in the formula for test statistic,

Comparing the test statistic value with the critical value obtained from z tables, the critical region ( for a left tailed test) is given by Z < .From Z tables is obtained as:

Here, the test statistic value -1.09 is greater than the tabled value for α = 0.08, Z = -1.41.Hence it does not lie in the rejection region.

Hence, the correct option would be:

No, since the test statistic is not 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.