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Chapter 10: Q. 7 (page 596)

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 82with a standard deviation of three, and a random sample of 25males had a mean score ofrole="math" localid="1650387947130" 76 with a standard deviation of four.

Short Answer

Expert verified

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

Step by step solution

01

Given information

It is believed that average grade of females is more than the males on an English essay in a specific school system.

31 random females had mean score of 82and standard deviation of 3.

25 random males had mean score of 76and standard deviation of 4.

02

Calculation

Now solving,

Assuming average grade of females as渭F.

Assuming average grade of makes as渭M.

The null and alternative hypothesis is obtained as :-

H0:渭F=渭MHa:渭F>渭M

This shows that this hypothesis testis for independent group means, population standard deviations, and/or variances unknown.

03

Final answer

This shows that this hypothesis testis for independent group means, population standard deviations, and/or variances unknown.

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Most popular questions from this chapter

Use the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1%significance level.

What is the sample mean difference?

Use the following informotion 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.

Which distribution (normal or Student's t) would you use for this hypothesis test?

The means of the number of revolutions per minute of two competing engines are to be compared. Thirty engines are randomly assigned to be tested. Both populations have normal distributions. Table given below shows the result. Do the data indicate that Engine 2 has higher RPM than Engine 1? Test at a 5%level of significance.

EngineSample mean number of RPMPopulation Standard Deviation
1150050
2160060

It is thought that teenagers sleep more than adults on average. A study is done to verify this. A sample of 16 teenagers has a mean of 8.9 hours slept and a standard deviation of 1.2. A sample of 12 adults has a mean of 6.9 hours slept and a standard deviation of 0.6.

Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.

Calculate the test statistic.
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