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Chapter 9: Q.81 (page 590)

Refer to Exercise 79. Construct and interpret a 95%confidence interval for the population mean M. What additional information does the confidence interval provide .

Short Answer

Expert verified

The confidence interval is (11.561,11.472).

Step by step solution

01

Given information

From question 79, The hardness data for a random sample of 20tablets are

02

Explanation


11.267


11.613
11.493
11.602
11.36
11.374
11.592
11.458
11.552
11.463
11.383
11.715
11.485
11.509
11.429

11.477

11.57
11.623
11.472
11.531
03

Calculate the confidence interval

The confidence interval for population mean is:

x¯-tα/2×sn<μ<x¯+tα/2×sn

The sample mean and standard deviation are 11.5164and 0.0950.

Degree of freedom:

localid="1650359464291" role="math" df=n-1=20-1=19

From critical value table, the t-value is 2.093.

The confidence interval is computed as:

x¯-tα/2×sn<μ<x¯+tα/2×sn

11.5164-2.096×0.095020<μ<11.5164+2.096×0.095020

(11.561,11.472)

The confidence interval is (11.561,11.472).

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Most popular questions from this chapter

The power of tomatoes The researchers who carried out the experiment in Exercise 75suspect that the large P-value (0.114) is due to low power.

(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise 75? Why?

(b) Explain two ways that the researchers could have increased the power of the test to detect .

(a) State hypotheses for a significance test to determine whether first responders are arriving within 8 minutes of the call more often. Be sure to define the parameter of interest.

(b) Describe a Type I error and a Type II error in this setting and explain the consequences of each.

(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.

(d) If you sustain a life-threatening injury due to a vehicle accident, you want to receive medical treatment as quickly as possible. Which of the two significance tests—H0:μ=6.7versusHa:μ<6.7 or the one from part (a) of this exercise—would you be

more interested in? Justify your answer.

Slow response times by paramedics, firefighters, and policemen can have serious consequences for accident victims. In the case of life-threatening injuries, victims generally need medical attention within 8 minutes of the accident. Several cities have begun to monitor emergency response times. In one such city, the mean response time to all accidents involving life-threatening injuries last year was M 6.7 minutes. Emergency personnel arrived within 8 minutes after 78% of all calls involving life-threatening injuries last year. The city manager shares this information and encourages these first responders to “do better.” At the end of the year, the city manager selects an SRS of 400 calls involving life-threatening injuries and examines the response times.

(a) State hypotheses for a significance test to determine whether the average response time has decreased. Be sure to define the parameter of interest.

(b) Describe a Type I error and a Type II error in this setting, and explain the consequences of each.

(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.

Stating hypotheses State the appropriate null and alternative hypotheses in each of the following cases.

(a) The average height of 18-year-old American women is 64.2inches. You wonder whether the mean height of this year's female graduates from a large local high school (over 3000students) differs from the national average. You measure an SRS of 48female graduates and find that X=63.1inches.

(b) Mr. Starnes believes that less than 75%of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of students at the school to help Mr. Starnes test his claim.

- Check conditions for carrying out a test about a population proportion or mean.

- Interpret P-values in context.

A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay \(100for the upgrade. For the upgrade to be profitable, the company needs to sell it to more than 20%of their customers. You contact a random sample of 60customers and find that 16 would be willing to pay \)100for the upgrade.

(a) Do the sample data give good evidence that more than 20%of the company’s customers are willing to purchase the upgrade? Carry out an appropriate test at the A=0.05significance level.

(b) Which would be a more serious mistake in this setting—a Type I error or a Type II error? Justify your answer.

(c) Other than increasing the sample size, describe one way to increase the power of the test in (a).
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