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A statistics student used a computer program to test the
Chapter 7, Problem 66E(choose chapter or problem)
A statistics student used a computer program to test the null hypothesis \(H_{0}: p=.5\) against the one-tailed alternative, \(H_{\mathrm{a}}: p>.5\). A sample of 500 observations are input into SPSS, which returns the following results: z = .44, two-tailed p-value = .33.
a. The student concludes, based on the p-value, that there is a 33% chance that the alternative hypothesis is true. Do you agree? If not, correct the interpretation.
b. How would the p-value change if the alternative hypothesis was two-tailed, \(H_{a}: p \neq .5\)? Interpret this p-value.
Questions & Answers
QUESTION:
A statistics student used a computer program to test the null hypothesis \(H_{0}: p=.5\) against the one-tailed alternative, \(H_{\mathrm{a}}: p>.5\). A sample of 500 observations are input into SPSS, which returns the following results: z = .44, two-tailed p-value = .33.
a. The student concludes, based on the p-value, that there is a 33% chance that the alternative hypothesis is true. Do you agree? If not, correct the interpretation.
b. How would the p-value change if the alternative hypothesis was two-tailed, \(H_{a}: p \neq .5\)? Interpret this p-value.
ANSWER:Step 1 of 3
It is given that a student tested the hypotheses
\(H_{0}: \mathrm{p}=0.5\) against \(H_{1}: \mathrm{p}>0.5 \text {. }\)
He had a sample of size n = 500.
The test statistic value obtained is z = 0.44 and the two tailed p-value is p = 0.33.
Using this we need to find the required values.