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Chapter 10: Q. T10.12 (page 699)

A random sample of 100of last year’s model of a certain popular car found that 20had a specific minor defect in the brakes. The automaker adjusted the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350of this year’s model found that 50had the minor brake defect.

a. Was the company’s adjustment successful? Carry out an appropriate test to support your answer. b. Based on your conclusion in part (a), which mistake—a Type I error or a Type II error—could have been made? Describe a possible consequence of this error.

Short Answer

Expert verified

a. The answer isP=P(Z>1.39)=P(Z<-1.39)=0.0823

b. Failure to reject the null hypothesis is a type II mistake.

Step by step solution

01

Part (a) Step 1: Given information

We have to tell about was the company’s adjustment successful

02

Part (a) Step 2: Explanation

It has been given that

x1=20,x2=50,n1=100,n2=350

p^2=x2n2=50350≈0.1429

z=p^1-p^2p^p1-p^p1n1+1n2=0.2-0.14290.1556(1-0.1556)1100+1350≈1.39

The values using the table

P=P(Z>1.39)=P(Z<-1.39)=0.0823

03

Part (b) Step 1: Given information

We have to tell possible consequence of this error.

04

Part (b) Step 2: Explanation

The null hypothesis H was not rejected.

  • Type I blunder: H should be rejected as a null hypothesis, if H 0H is true as the null hypothesis.

Failure to reject the null hypothesis is a type II mistake.

If the null hypothesis H is false, then

It's only feasible that we made.

  • Type II error because we didn't reject the null hypothesis H .

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Most popular questions from this chapter

A quiz question gives random samples of n=10observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9degrees of freedom to calculate a 95%confidence interval for the difference in the two population means. Janelle uses her calculator's two-sample t Interval with 16.87degrees of freedom to compute the 95%confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?

(a) Tom's confidence interval is wider.

(b) Janelle's confidence Interval is wider.

(c) Both confidence Intervals are the same.

(d) There is insufficient information to determine which confidence interval is wider.

(e) Janelle made a mistake, degrees of freedom has to be a whole number.

Ice cream For a statistics class project, Jonathan and Crystal held an ice-cream-eating contest. They randomly selected 29 males and 35 females from their large high school to participate. Each student was given a small cup of ice cream and instructed to eat it as fast as possible. Jonathan and Crystal then recorded each contestant’s gender and time (in seconds), as shown in the dot plots.

Do these data give convincing evidence of a difference in the population means at the α=0.103051526=0.200=20.0%α=0.10 significance level?

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

Two samples or paired data? In each of the following settings, decide whether you should use two-sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean difference. Explain your choice.

a. To compare the average weight gain of pigs fed two different diets, nine pairs of pigs were used. The pigs in each pair were littermates. A coin toss was used to decide which pig in each pair got Diet A and which got Diet B.

b. Separate random samples of male and female college professors are taken. We wish to compare the average salaries of male and female teachers.

c. To test the effects of a new fertilizer, 100 plots are treated with the new fertilizer, and 100 plots are treated with another fertilizer. A computer’s random number generator is used to determine which plots get which fertilizer.

Literacy Refer to Exercise 2.

a. Find the probability that the proportion of graduates who pass the test is at most 0.20higher than the proportion of dropouts who pass, assuming that the researcher’s report is correct.

b. Suppose that the difference (Graduate – Dropout) in the sample proportions who pass the test is exactly 0.20. Based on your result in part (a), would this give you reason to doubt the researcher’s claim? Explain your reasoning.

Suppose the true proportion of people who use public transportation to get to work in the Washington, D.C. area is 0.45. In a simple random sample of 250people who work in Washington, about how far do you expect the sample proportion to be from the true proportion?

a. 0.4975

b. 0.2475

c. 0.0315

d. 0.0009

e.0
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