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Chapter 10: Q. 11 (page 596)

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.

Short Answer

Expert verified

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

Step by step solution

01

Given information

Teenagers are thought to sleep more than adults on average. The average number of hours worked by 16 teenagers was 8.9, with a standard deviation of 1.2.

The mean for a group of 12 adults is 6.9 hours, with a standard deviation of 0.6.

02

The most appropriate hypothesis test for the supplied data.

Assuming average hours of sleep for teenagers as 渭T

Assuming an average of eight hours of sleep渭A

The alternative and null hypothesis are as follows:

H0:渭T=渭AHa:渭T>渭A

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

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Most popular questions from this chapter

At the 1% significance level, what is your conclusion?

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?

93. A study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are 1.5811 years and 1 year, respectively. The following data are collected. The California state university system students took on average 4.5 years with a standard deviation of 0.8. The private university students took on average 4.1 years with a standard deviation of 0.3.

96. Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 31 mpg with a standard deviation of seven mpg. Thirty one non-hybrid sedans get a mean of 22mpg with a standard deviation of four mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test to evaluate the manufacturers claim.

Adults aged 18 years old and older were randomly selected for a survey on obesity. Adults are considered obese if their body mass index (BMI) is at least 30. The researchers wanted to determine if the proportion of women who are obese in the south is less than the proportion of southern men who are obese. The results are shown in Table 10.27. Test at the 1% level of significance.


Number who are obeseSample size
Men42769155,525
Women67169248,775
See all solutions

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