(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
"H_1: p\\not=0.05"
This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used.
(2) Rejection Region
If the significance level is not stated use "\\alpha=0.05."
The critical value for a two-tailed test is "z_c=1.96."
The rejection region for this two-tailed test is "R=\\{z:|z|>1.96 \\}"
(3) Test Statistics
"\\hat{p}={x \\over n}={5 \\over 50}=0.1"The z-statistic is computed as follows:
(4) Decision about the null hypothesis
Since it is observed that "|z|=1.622<1.96=z_c," it is then concluded that the null hypothesis is not rejected.
(5) Conclusion
It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion "p" is different than "p_0," at the "\\alpha=0.05" significance level.
Confidence Interval
The 95% confidence interval for "p" is: "0.017<p<0.183."
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