Question

(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 population standard deviation of 4.1 minutes. At α = 0.04, what type of test is this and can you support the organizations’ claim using the test statistic?

Claim is the alternative, reject the null so support the claim as test statistic (-0.30) is in the rejection region defined by the critical value (-2.05)

Claim is the null, reject the null so cannot support the claim as test statistic (-0.30) is in the rejection region defined by the critical value (1.75)

Claim is the alternative, fail to reject the null so cannot support the claim as test statistic (-0.30) 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 (-0.30) is not in the rejection region defined by the critical value (1.75)

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

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 null, fail to reject the null and 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)

Answer 1

(CO7)

H0:Null Hypothesis: 16

HA:Alternative Hypothesis: 16 (Claim)

SE = /

= 4.1/

= 0.6565

Test Statistic is:
Z = (15.8- 16)/0.6565 =- 0.30

= 0.04

From Table, critical value oof Z = - 1.75

Since calculated value of Z is greater than critical value of Z, the difference is not significant. Fail to reject null hypothesis.

So,

Correct option:

Claim is the alternative, fail to reject null so cannot support the claim as test statistic (-0.30) is not in rejection region defined by the critical value (-1.75)

(CO7)

H0; Null Hypothesis: = 6.800

HA: Alternative Hypothesis: 6.800

SE = /

= 0.05/ = 0.0080

Test statistic is:

Z= (6.810 - 6.800)/0.0080 = 1.2490

Table of Area Under Standard Normal Curve gives area = 0.3944

So,

P - Value =(0.5 - 0.3944) X 2= 0.212

Since P - value is greater than = 0.08, the difference is not significant. Fail to reject null hypothesis.

So,

Correct option:

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