Question

multiple choice. choose the one alternative that best completes the statement or answers the question.
find the p - value for the indicated hypothesis test.

1. in a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. find the p - value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%.

a) - 0.2843 b) 0.2843 c) 0.5686 d) 0.2157

1. a manufacturer claims that fewer than 6% of its fax machines are defective. in a random sample of 97 such fax machines, 5% are defective. find the p - value for a test of the manufacturers claim.

a) 0.3264 b) 0.1591 c) 0.3409 d) 0.1736

1. a nationwide study of american homeowners revealed that 65% have one or more lawn mowers. a lawn equipment manufacturer, located in omaha, feels the estimate is too low for households in omaha. find the p - value for a test of the claim that the proportion with lawn mowers in omaha is higher than 65%. among 497 randomly selected homes in omaha, 340 had one or more lawn mowers.

a) 0.1118 b) 0.0252 c) 0.0505 d) 0.0559

1. a random sample of 139 forty - year - old men contains 26% smokers. find the p - value for a test of the claim that the percentage of forty - year - old men that smoke is 22%.

a) 0.2542 b) 0.1271 c) 0.2802 d) 0.1401

Explanation:

Step1: Calculate sample proportion

The sample proportion \(\hat{p}=\frac{x}{n}\), where \(x = 8\) and \(n=88\). So \(\hat{p}=\frac{8}{88}\approx0.0909\). The hypothesized proportion \(p = 0.11\), and \(q=1 - p=0.89\).

Step2: Calculate test statistic \(z\)

The formula for the test statistic in a proportion test is \(z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}\). Substitute the values: \(z=\frac{0.0909 - 0.11}{\sqrt{\frac{0.11\times0.89}{88}}}\approx\frac{- 0.0191}{\sqrt{\frac{0.0979}{88}}}\approx\frac{-0.0191}{0.0333}\approx - 0.57\)

Step3: Find P - value

Since this is a two - tailed test (claim is \(p = 0.11\)), the P - value is \(2P(Z\lt - 0.57)\). Using the standard normal table, \(P(Z\lt - 0.57)=0.2843\), so \(P - value=2\times0.2843 = 0.5686\)

Answer:

C. 0.5686