Suppose we are constructing a confidence interval using repeated tests of signif
ID: 3272898 • Letter: S
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
0.007
Proportion = 0.53
0.602
Proportion = 0.46
0.012
Proportion = 0.54
0.124
Proportion = 0.47
0.045
Proportion = 0.55
0.084
Proportion = 0.48
0.079
Proportion = 0.56
0.052
Proportion = 0.49
0.121
Proportion = 0.57
0.034
Proportion = 0.50
0.254
Proportion = 0.58
0.019
Proportion = 0.51
0.643
Proportion = 0.59
0.012
Proportion = 0.52
0.986
Proportion = 0.60
0.004
Using the results from the table, give a 95% AND 99% Confidence interval
Null
p-value
Null
p-value
Proportion = 0.45
0.007
Proportion = 0.53
0.602
Proportion = 0.46
0.012
Proportion = 0.54
0.124
Proportion = 0.47
0.045
Proportion = 0.55
0.084
Proportion = 0.48
0.079
Proportion = 0.56
0.052
Proportion = 0.49
0.121
Proportion = 0.57
0.034
Proportion = 0.50
0.254
Proportion = 0.58
0.019
Proportion = 0.51
0.643
Proportion = 0.59
0.012
Proportion = 0.52
0.986
Proportion = 0.60
0.004
Explanation / Answer
First we create a 95% confidence interval, in this case the significance level is:
a = 0.05
So any value of null for which the corresponding p-value is greater than 0.05 would be considered plausible, otherwise not.
So we have to look for those values for which the p-value is greater than 0.05
We see that the values of the null in the range 0.48 to 0.56 have their corresponding p-values greater than 0.05
So the 95% confidence interval is:
0.48 < p95% < 0.56
Next we create a 99% confidence interval, in this case the significance level is:
a = 0.01
So any value of null for which the corresponding p-value is greater than 0.01 would be considered plausible, otherwise not.
So we have to look for those values for which the p-value is greater than 0.01
We see that the values of the null in the range 0.46 to 0.59 have their corresponding p-values greater than 0.01
So the 99% confidence interval is:
0.46 < p99% < 0.59
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