Question

1.

(CO7) An advocacy group claims that the mean braking distance of a certain type of tire is 75 feet when the car is going 40 miles per hour. In a test of 45 of these tires, the braking distance has a mean of 78 and a standard deviation of 5.9 feet. Find the standardized test statistic and the corresponding p-value.

z-test statistic = -3.41, p-value = 0.0003

z-test statistic = 3.41, p-value = 0.0003

z-test statistic = 3.41, p-value = 0.0006

z-test statistic = -3.41, p-value = 0.0003

2.

(CO7) 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 standard deviation of 62 hours. At an α=0.05, can you support the company’s claim using the test statistic?

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)

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)

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)

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)

3.

(CO7) 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 standard deviation of 1.4 minutes. At α = 0.04, can you support the organizations’ claim using the test statistic?

Claim is the null, reject the null so cannot support the claim as test statistic (-0.89) is in the rejection region defined by the critical value (-2.05)

Claim is the alternative, fail to reject the null so cannot support the claim as test statistic (-0.89) is not in the rejection region defined by the critical value (-1.75)

Claim is the null, fail to reject the null so support the claim as test statistic (-0.89) is not in the rejection region defined by the critical value (-1.75)

Claim is the alternative, reject the null so support the claim as test statistic (-0.89) is in the rejection region defined by the critical value (-2.05)

4.

(CO7) 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 standard deviation of 0.05 inches. At α=0.08, can you support the manufacturer’s claim using the p value?

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

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

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

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

Answer 1

1)

test statitic =(x-mean)*sqrt(n)/std deviaiton =(78-75)*sqrt(45)/5.9 =3.41

z-test statistic = 3.41, p-value = 0.0006

2)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

3)

Claim is the alternative, fail to reject the null so cannot support the claim as test statistic (-0.89) is not in the rejection region defined by the critical value (-1.75)

4)

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