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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,μ0=9

02

Explanation

For this situation, the test statistic formula is t=X-μ0sn

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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