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Chapter 10: Q. 10.11 (page 587)

A study was conducted to investigate how effective a new diet was in lowering cholesterol. Results for the

randomly selected subjects are shown in the table. The differences have a normal distribution. Are the subjects鈥�

cholesterol levels lower on average after the diet? Test at the 5%level.

SubjectABCDEFGHI
Before209210205198216217238240222
After199207189209217202211223201

Short Answer

Expert verified

There is sufficient evidence to conclude that the diet lowers cholesterol.

Step by step solution

01

Given information

Given the results for the randomly selected subjects. Test at 5%level.

02

Calculation

The null and alternative hypothesis are :

H0:渭d=0Ha:渭d<0

The significant level, 伪=5%=0.05.

The p-value is 0.0130, which is lower than the significant level, so we reject the null hypothesis.

Hence, there is sufficient evidence to conclude that the diet lowers cholesterol.

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Most popular questions from this chapter

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.

In symbols, what is the random variable of interest for this test?

Ten individuals went on a low鈥揻at diet for 12 weeks to lower their cholesterol. The data are recorded in Table 10.30. Do you think that their cholesterol levels were significantly lowered?

Starting cholesterol levelEnding cholesterol level140140220230110120240220200190180150190200360300280300260240

Use the following information to answer the next two exercises. A new AIDS prevention drug was tried on a group of 224 HIV positive patients. Forty-five patients developed AIDS after four years. In a control group of 224 HIV positive patients, 68 developed AIDS after four years. We want to test whether the method of treatment reduces the proportion of patients that develop AIDS after four years or if the proportions of the treated group and the untreated group stay the same.

Let the subscript t=treated patient and ut=untreated patient.

Use the following information to answer the next five exercises. A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table 10.21. The 鈥渂efore鈥� value is matched to an 鈥渁fter鈥� value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level.

What conclusion can you draw about the software patch?

100. We are interested in whether the proportions of female suicide victims for ages 15 to 24 are the same for the whites and the blacks races in the United States. We randomly pick one year, 1992, to compare the races. The number of suicides estimated in the United States in 1992 for white females is 4,930 . Five hundred eighty were aged 15 to 24 . The estimate for black females is 330 . Forty were aged 15 to 24 . We will let female suicide victims be our population.

Comparing Two Independent Population Proportions.

Use the following informotion for the next five exercises. Two types of phone operating system are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1 had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with

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Is this a test of means or proportions?
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