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Chapter 10: Q. 7 (page 596)

Use the following information to answer the next 15exercises: Indicate if the hypothesis test is for

a. independent group means, population standard deviations, and/or variances known

b. independent group means, population standard deviations, and/or variances unknown

c. matched or paired samples

d. single mean

e. two proportions

f. single proportion

It is believed that the average grade on an English essay in a particular school system for females is higher than for males. A random sample of 31females had a mean score of 82 with a standard deviation of three, and a random sample of 25 males had a mean score of 76 with a standard deviation of four

Short Answer

Expert verified

The test is for unknown variances, independent group means, and population standard deviations.

Step by step solution

01

Given information

Females are thought to get a higher average grade on an English essay in a certain educational system than males.

The mean score of 31random females was 82, with a standard deviation of3.

The mean score of 31random females was82, with a standard deviation of 4.

02

Explanation

Assuming a female's average grade is 渭F

Assuming a male's average grade is 渭M

The null and alternative hypothesis is given as

H0:渭F=渭MHa:渭F>渭M

This demonstrates that the hypothesis test is valid for independent group means, population standard deviations, and unknown variances.

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Most popular questions from this chapter

Use the following information to answer next five exercises. A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the 1% significance level

What is the sample mean difference?

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State the null and alternative hypotheses

Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.

19. Is this a test of means or proportions?

Researchers conducted a study to find out if there is a difference in the use of eReaders by different age groups. Randomly selected participants were divided into two age groups. In the 16- to 29-year-old group, 7%of the 628surveyed use eReaders, while of the 2,309participants 30years old and older use eReaders.

95. A group of transfer bound students wondered if they will spend the same mean amount on texts and supplies each year at their four-year university as they have at their community college. They conducted a random survey of 54 students at their community college and 66 students at their local four-year university. The sample means were \(947 and \)1,011, respectively. The population standard deviations are known to be \(254and \)87, respectively. Conduct a hypothesis test to determine if the means are statistically the same.
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