Statistics Homework Help

1.A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 720 hours. A

random sample of 51 light bulbs as a mean of 701.6 hours with a population standard deviation of 62 hours. At an α=0.05, can you support the company’s claim using the test statistic?

A.Claim is the alternative, reject the null and support claim as test statistic (-2.12) is not in the rejection region defined by the critical value (-1.96)

B.Claim is the alternative, fail to reject the null and cannot support claim as the test statistic (-2.12) is in the rejection region defined by the critical value (-1.96)

C.Claim is the null, reject the null and cannot support claim as test statistic (-2.12) is in the rejection region defined by the critical value (-1.645)

D.Claim is the null, fail to reject the null and cannot support claim as test statistic (-2.12) is not in the rejection region defined by the critical value (-1.645)

2. A restaurant claims the customers receive their food in less than 16 minutes. A random sample of 39 customers finds a mean wait time for food to be 15.8 minutes with a population standard deviation of 4.9 minutes. At α = 0.04, can you support the organizations’ claim using the test statistic?

A.Claim is the alternative, fail to reject the null so cannot support the claim as test statistic (-0.25) is not in the rejection region defined by the critical value (-1.75)

B.Claim is the null, fail to reject the null so support the claim as test statistic (-0.25) is not in the rejection region defined by the critical value (-1.75)

C.Claim is the null, reject the null so cannot support the claim as test statistic (-0.25) is in the rejection region defined by the critical value (-2.05)

D.Claim is the alternative, reject the null so support the claim as test statistic (-0.25) is in the rejection region defined by the critical value (-2.05)

3.A manufacturer claims that their calculators are 6.800 inches long. A random sample of 39 of their calculators finds they have a mean of 6.810 inches with a population standard deviation of 0.05 inches. At α=0.08, can you support the manufacturer’s claim using the p value?

A.Claim is the null, fail to reject the null and support claim as p-value (0.106) is greater than alpha (0.08)

B.Claim is the alternative, fail to reject the null and support claim as p-value (0.212) is greater than alpha (0.08)

C.Claim is the alternative, reject the null and cannot support claim as p-value (0.106) is greater than alpha (0.08)

D.Claim is the null, reject the null and cannot support claim as p-value (0.212) is greater than alpha (0.08)

4. A travel analyst claims that the mean room rates at a three-star hotel in Chicago is greater than $152. In a random sample of 36 three-star hotel rooms in Chicago, the mean room rate is $160 with a population standard deviation of $41. At α=0.10, can you support the analyst’s claim using the p-value?

A.Claim is the alternative, reject the null as p-value (0.121) is not less than alpha (0.10), and can support the claim

B.Claim is the null, reject the null as p-value (0.121) is not less than alpha (0.10), and cannot support the claim

C.Claim is the null, fail to reject the null as p-value (0.121) is not less than alpha (0.10), and cannot support the claim

D.Claim is the alternative, fail to reject the null as p-value (0.121) is not less than alpha (0.10), and cannot support the claim

5.A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon. A random sample of 7 cars has a mean gas mileage of 23 miles per gallon and a standard deviation of 2.4 miles per gallon. At α=0.05, can you support the company’s claim assuming the population is normally distributed?

A.Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the alternative, so is supported

B.Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

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

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

6.A state Department of Transportation claims that the mean wait time for various services at its different location is more than 6 minutes. A random sample of 16 services at different locations has a mean wait time of 9.5 minutes and a standard deviation of 7.3 minutes. At α=0.01, can the department’s claim be supported assuming the population is normally distributed?

A.Yes, since p of 0.037 is greater than 0.01, fail to reject the null. Claim is null, so is supported

B.No, since p of 0.037 is greater than 0.01, reject the null. Claim is null, so is not supported

C.No, since p of 0.037 is greater than 0.01, fail to reject the null. Claim is alternative, so is not supported

D.Yes, since p of 0.037 is less than 0.07, reject the null. Claim is alternative, so is supported

7.A used car dealer says that the mean price of a three-year-old sport utility vehicle in good condition is $18,000. A random sample of 20 such vehicles has a mean price of $18,450 and a standard deviation of $1860. At α=0.08, can the dealer’s claim be supported assuming the population is normally distributed?

A.No, since the test statistic of 1.08 is close to the critical value of 1.24, the null is not rejected. The claim is the null, so is supported

B.Yes, since the test statistic of 1.08 is in the rejection region defined by the critical value of 1.46, the null is rejected. The claim is the null, so is supported

C.Yes, since the test statistic of 1.08 is not in the rejection region defined by the critical value of 1.85, the null is not rejected. The claim is the null, so is supported

D.No, since the test statistic of 1.08 is in the rejection region defined by the critical value of 1.85, the null is rejected. The claim is the null, so is not supported