Suppose that researcher A forms a two-sided 95 percent confidence interval to estimate µ (the population mean). The result is L =.30 and U = .60. Researcher B, using the same data, performs a two-tailed hypothesis test of the null hypothesis µ = .45. Which of the following is true concerning the result of the hypothesis test?  Researcher B rejects the null hypothesis.  Researcher B fails to reject the null hypothesis.  Not enough information is given to know if researcher B rejects or fails to reject.  Researcher B will make a Type I error.

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Asked Oct 15, 2019
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Suppose that researcher A forms a two-sided 95 percent confidence interval to estimate µ (the population mean). The result is L =.30 and U = .60. Researcher B, using the same data, performs a two-tailed hypothesis test of the null hypothesis µ = .45. Which of the following is true concerning the result of the hypothesis test?

   

Researcher B rejects the null hypothesis.

   

Researcher B fails to reject the null hypothesis.

   

Not enough information is given to know if researcher B rejects or fails to reject.

   

Researcher B will make a Type I error.

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Expert Answer

Step 1

State the hypotheses:

From the given information, the researcher A constructed 95% confidence interval to estimate population mean. The lower limit of confidence interval is 0.30 and upper limit of confidence interval is 0.60.  The researcher B assumed population mean value is 0.45.

Null hypothesis:

µ=0.45

Alternative Hypothesis:

µ≠0.45

Step 2

Rejection rule based on confidence interval:

If the hypothesized value of the parameter lies in the confidence interval of that parameter, then do not reject the null hypothesis.

Step 3

The conclusion is stated below:

The 95% confidence interval to estimate population mean is (0.30, 060). The population mean (µ=0.45) value lies in the confidence interval so do not reject the null hypothesis.

Therefore,  ...

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