Question

Suppose we are constructing a confidence interval using repeated tests of significance to develop an interval of plausible values. Using two-sided tests each time with the following null hypotheses, we obtain the resulting p-values.

Null p-value Null p-value
Proportion = 0.45 0.014 Proportion = 0.53 0.787
Proportion = 0.46 0.032 Proportion = 0.54 0.572
Proportion = 0.47 0.062 Proportion = 0.55 0.373
Proportion = 0.48 0.126 Proportion = 0.56 0.142
Proportion = 0.49 0.371 Proportion = 0.57 0.077
Proportion = 0.50 0.598 Proportion = 0.58 0.042
Proportion = 0.51 0.733 Proportion = 0.59 0.021
Proportion = 0.52 0.986 Proportion = 0.60 0.003


Using the results from the table, give a 90% confidence interval.

Using the results from the table, give a 95% confidence interval.

Answer 1

Check the explanation

Explanation:

90% confidence interval:

For 90% confidence level, \alpha=1-0.90=0.10.

take a look at p-values you'll notice that they are just greater than 0.10 on both upper and lower side. Those proportions would be 90% confidence interval.

Kindle check the first image for the figure table

p-value = 0.126 is just above 0.10 on lower side and p-value = 0.142 is just above 0.10 on upper side. Therefore, the 90% confidence interval is (0.48, 0.56).

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95% confidence interval:

For 95% confidence level, \alpha=1-0.95=0.05.

take a look at p-values you'll notice that they are just greater than 0.05 on both upper and lower side. Those proportions would be 95% confidence interval.

Kindle check the second image for the figure table

p-value = 0.062 is just above 0.05 on lower side and p-value = 0.077 is just above 0.05 on upper side. Therefore, the 95% confidence interval is (0.47, 0.57).