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To test H0: ? = 20 versus H1: ? < 20, a simple random

Chapter 6, Problem 7AYU

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QUESTION:

To test \(H_{0}: \mu=20\) versus \(H_{1}: \mu<20\), a simple random sample of size n = 18 is obtained from a population that is known to be normally distributed.

(a) If \(\bar{x}=18.3\) and s = 4.3, compute the test statistic.

(b) Draw a f-distribution with the area that represents the P-value shaded.

(c) Approximate and interpret the P-value.

(d) If the researcher decides to test this hypothesis at the \(\alpha=0.05\) level of significance, will the researcher reject the null hypothesis? Why?

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QUESTION:

To test \(H_{0}: \mu=20\) versus \(H_{1}: \mu<20\), a simple random sample of size n = 18 is obtained from a population that is known to be normally distributed.

(a) If \(\bar{x}=18.3\) and s = 4.3, compute the test statistic.

(b) Draw a f-distribution with the area that represents the P-value shaded.

(c) Approximate and interpret the P-value.

(d) If the researcher decides to test this hypothesis at the \(\alpha=0.05\) level of significance, will the researcher reject the null hypothesis? Why?

ANSWER:

Answer :

Step 1 :

Given,

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