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Chapter 10: Q. 29 (page 670)

According to sleep researchers, if you are between the ages of 12and 18years old, you need 9hours of sleep to be fully functional. A simple random sample of 28students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9hours, with a standard deviation of 2.1hours.

Which of the following is the test statistic for the hypothesis test?

(a)t=7.9-92.128

(b)t=9-7.92.128

(c)t=7.9-92.128

(d)t=7.9-92.127

(e)t=9-7.92.127

Short Answer

Expert verified

The test statistic for the hypothesis test is (a)t=7.9-92.128

Step by step solution

01

Given information

We are given that if you are between the ages of 12and 18years old.The mean of the responses was 7.9hours, with a standard deviation of 2.1 hours. We have to find the test statistic for the hypothesis test

02

Simplify

As we know,

t=X-μ0sn

Where,

μ0=9(Hypothesized claim)

X=7.9(Sample mean )

n=28(Sample size)

s=2.1(Sample standard deviation)

By putting the values in above formula

t=7.9-92.128

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Most popular questions from this chapter

Quality control (2.2,5.3,6.3)Many manufacturing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the production shift. Assuming that the process is working properly, the mean measurements from these random samples will vary Normally around the target mean μ, with a standard deviation of σ. For each question that follows, assume that the process is working properly.

(a) What's the probability that at least one of the next two sample means will fall more than 2σfrom the target mean μ? Show your work.

(b) What's the probability that the first sample mean that is greater than μ+2σis the one from the fourth sample taken?

(c) Plant managers are trying to develop a criterion for determining when the process is not working properly. One idea they have is to look at the 5 most recent sample means. If at least 4of the 5 fall outside the interval(μ-σ,μ+σ), they will conclude that the process isn't working. Is this a reasonable criterion? Justify your answer with an appropriate probability.

Refer to Exercise 36. Suppose we select independent SRSs of 16 young men and 9 young women and calculate the sample mean heights xMandxW

(a) Describe the shape, center, and spread of the sampling distribution of xM-xW

(b) Find the probability of getting a difference in sample means x¯M-x¯Wthat’s greater than or equal to 2inches. Show your work.

(c) Should we be surprised if the sample mean height for the young women is more than 2inches less than the sample mean height for the young men? Explain.

Are teens or adults more likely to go online daily? The Pew Internet and American Life Project asked a random sample of 800 teens and a separate random sample of 2253 adults how often they use the Internet. In these two surveys, 63% of teens and 68%of adults said that they go online every day. Construct and interpret a 90% confidence interval for p1-p2?

Refer to Exercise16.

(a) Carry out a significance test at the α=0.05level.

(b) Construct and interpret a 95%confidence interval for the difference between the population proportions. Explain how the confidence interval is consistent with the results of the test in part (a).

Pat wants to compare the cost of one- and two-bedroom apartments in the area of her college campus. She collects data for a random sample of 10 advertisements of each type. The table below shows the rents (in dollars per month) for the selected apartments.

Pat wonders if two-bedroom apartments rent for significantly more, on average than one-bedroom apartments. She decides to perform a test of H0:μ1=μ2 versus Ha:μ1<μ2, where μ1 and μ2 are the true mean rents for all one-bedroom and two-bedroom aparaments, respectively, near the campus.

(a) Name the appropriate test and show that the conditions for carrying out this test are met.

(b) The appropriate test from part (a) yields a P-value of 0.058. Interpret this P-value in context.

(c) What conclusion should Pat draw at theα=0.05 significance level? Explain.
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