# (CO7) A restaurant claims the

(CO7) A restaurant claims the customers receive their food inless than 16 minutes. A random sample of 39 customers finds a meanwait time for food to be 15.8 minutes with a population standarddeviation of 4.1 minutes. At α = 0.04, what type of test is thisand can you support the organizations’ claim using the teststatistic?

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

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

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

Claim is the null, fail to reject the null so support the claimas test statistic (-0.30) is not in the rejection region defined bythe critical value (1.75)

(CO7) A manufacturer claims that their calculators are 6.800inches long. A random sample of 39 of their calculators finds theyhave a mean of 6.810 inches with a population standard deviation of0.05 inches. At α=0.08, can you support the manufacturer’s claimusing the p value?

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

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

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

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

Answer:

(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 nullhypothesis.

So,

Correct option:

**Claim is the alternative, fail to reject null so cannotsupport the claim as test statistic (-0.30) is not in rejectionregion 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, thedifference is not significant. Fail to reject null hypothesis.

So,

Correct option:

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