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Chapter 10: Q. 29 (page 705)

According to sleep researchers, if you are between the ages of 12and 18years old, you need 9 hours of sleep to function well. 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 standardized test statistic for the hypothesis test ?

  1. localid="1654221307488" t=7.9-92.128andt=7.9-92.128
  2. t=9-7.92.128andt=9-7.92.128
  3. t=7.9-92.128and t=7.9-92.128
  4. localid="1654221494579" t=7.9-92.127andt=7.9-92.127
  5. localid="1654221497857" t=9-7.92.127andt=9-7.92.127

Short Answer

Expert verified

Option (a) is correct answer :t=7.9-92.128,t=7.9-92.128

Step by step solution

01

Given Information

We are given following information:

No. of samples, n=28

Sample mean , X=7.9

Sample standard deviation, s=2.1

Hypothesized value,渭0=9

02

Explanation

For this situation, the test statistic formula is t=X-渭0sn

This assumes the data is normally distributed with unknown population standard deviation.

Calculating standardized test statistic for present case we get.;

t=7.9-92.128

Hence, option (a) is correct option.

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Most popular questions from this chapter

Have a ball! Can students throw a baseball farther than a softball? To find out, researchers conducted a study involving 24randomly selected students from a large high school. After warming up, each student threw a baseball as far as he or she could and threw a softball as far as he she could, in a random order. The distance in yards for each throw was recorded. Here are the data, along with the difference (Baseball 鈥� Softball) in distance thrown, for each student:

a. Explain why these are paired data.

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c. State appropriate hypotheses for performing a test about the true mean difference. Be sure to define any parameter(s) you use.

d. Explain why the Normal/Large Sample condition is not met in this case. The mean difference (Baseball鈭扴oftball) in distance thrown for these 24students is xdiff = 6.54yards. Is this a surprisingly large result if the null hypothesis is true? To find out, we can perform a simulation assuming that students have the same ability to throw a baseball and a softball. For each student, write the two distances thrown on different note cards. Shuffle the two cards and designate one distance to baseball and one distance to softball. Then subtract the two distances (Baseball鈭扴oftball) . Do this for all the students and find the simulated mean difference. Repeat many times. Here are the results of 100trials of this simulation

e. Use the results of the simulation to estimate the P-value. What conclusion would you draw ?

I want red!A candy maker offers Child and Adult bags of jelly beans with

different color mixes. The company claims that the Child mix has 30%red jelly beans, while the Adult mix contains 15%red jelly beans. Assume that the candy maker鈥檚 claim is true. Suppose we take a random sample of 50jelly beans from the Child mix and a separate random sample of 100jelly beans from the Adult mix. Let p^Cand p^Abe the sample proportions of red jelly beans from the Child and

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b. Find the mean of the sampling distribution.

c. Calculate and interpret the standard deviation of the sampling distribution.

Bird eggs A researcher wants to see if birds that build larger nests lay larger eggs. She selects two random samples of nests: one of the small nests and the other of large nests. Then she weighs one egg (chosen at random if there is more than one egg) from each nest. A 95% confidence interval for the difference (Large 鈭� Small) between the mean mass (in

grams) of eggs in small and large nests is 1.6卤2.0 role="math" localid="1654714720708" 3051526=0.200=20.0%1.6卤2.0

a. Does the interval provide convincing evidence of a difference in the true mean egg mass of birds with small nests and birds with large nests? Explain your answer.

b. Does the interval provide convincing evidence that the true mean egg mass of birds with small nests and birds with large nests is the same? Explain your answer.

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a. the paired t test for 渭diff3051526=0.200=20.0%渭diff.

b. the one-sample z test for p.

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