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Q.7

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The Practice of Statistics for AP
Found in: Page 595
The Practice of Statistics for AP

The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339

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Short Answer

Fonts and reading ease Does the use of fancy type fonts slow down the reading of text on a computer screen? Adults can read four paragraphs of text in the common Times New Roman font in an average time of 22 seconds. Researchers asked a random sample of 24 adults to read this text in the omate font named Gigi. Here are their times, in seconds:

23.221.228.927.729.127.316.122.625.634.223.926.8
20.534.321.432.626.234.131.524.623.028.624.428.1

Do these data provide good evidence that the mean reading time for Gigi is greater than 22seconds? Carry out an appropriate test to help you answer this question.

- Use a confidence interval to draw a conclusion for a two-sided test about a population mean.

Yes, there is sufficient evidence to conclude that the mean reading time for Gigi is more than 22 seconds,

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step-1 Given Information

Given in the question that,

23.221.228.927.729.127.316.122.625.634.223.926.8
20.534.321.432.626.234.131.524.62328.624.428.1

we have to find out that Do these data provide good evidence that the mean reading time for Gigi is greater than 22seconds.

Step-2 Explanation

The formula used to compute the test statistic is:

t=x¯-μsn

The null and alternative hypothesis are:

H0:μ=22

Hα:μ>22

Assume level of significance to be 0.05

the obtained output is:

The significance level is less than thep-value(0.000) in this case. As a result, the null hypothesis is ruled out. As a result, there is enough information to indicate that Gigi's average reading time is greater than 22 seconds.

Most popular questions for Math Textbooks

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.

Your company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements. Based on the sample results, the device determines whether there is significant evidence that the individual’s actual mean systolic pressure is greater than 130. If so, it recommends that the person seek medical attention.

(a) State appropriate null and alternative hypotheses in this setting. Be sure to define your parameter.

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

(c) The blood pressure device can be adjusted to decrease one error probability at the cost of an increase in the other error probability. Which error probability would you choose to make smaller, and why?

A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for 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 60 customers and find that 16 would be willing to pay $100 for 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=0.05 significance 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).

Tests and CIs The P-value for a one-sided test of the null hypothesisH0:μ=15 is 0.03.

(a) Does the 99% confidence interval for μ include 15 ? Why or why not?

(b) Does the 95% confidence interval for μinclude 15? Why or why not?

Sweetening colas Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. From experience, the population distribution of sweetness losses will be close to Normal. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of 10 batches of a new cola recipe:

2.0 0.4 0.7 2.0 -0.4 2.2 -1.3 1.2 1.1 2.3

Are these data good evidence that the cola lost sweetness? Carry out a test to help you answer this question.
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