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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 15 exercises: 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

A new WiFi range booster is being offered to consumers. A researcher tests the native range of 12 different routers under the same conditions. The ranges are recorded. Then the researcher uses the new WiFi range booster and records the new ranges. Does the new WiFi range booster do a better job?

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.

Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. Table 10.18 shows the result. Scouters believe that Rodriguez pitches a speedier fastball.

A study is done to determine if Company A retains its workers longer than Company B. Company A samples 15workers, and their average time with the company is five years with a standard deviation of 1.2.Company B samples 20workers, and their average time with the company is 4.5yearswith a standard deviation of 0.8.The populations are normally distributed.

a. Are the population standard deviations known?

b. Conduct an appropriate hypothesis test. At the 5%significance level, what is your conclusion?

Use the following information to answer the next three exercises: A study is done to determine which of two soft drinks has more sugar. There are 13 cans of Beverage A in a sample and six cans of Beverage B. The mean amount of sugar in Beverage A is 36 grams with a standard deviation of 0.6 grams. The mean amount of sugar in Beverage B is 38 grams with a standard deviation of 0.8 grams. The researchers believe that Beverage B has more sugar than Beverage A, on average. Both populations have normal distributions.

Are standard deviations known or unknown?
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