Q7
Given that "n=100, \\hat{p}=70\/100=0.7"
90% confidence interval: "z_{\\alpha\/2}=1.645"
"CI(proportion)=(0.6245,0.7755)"
(2) (0.6246; 0.7754)
Q8
95% confidence interval: "z_{\\alpha\/2}=1.96"
(1) 0:6102
Q9
The following null and alternative hypotheses need to be tested:
"H_0:\\pi=0.75"
"H_1:\\pi\\not=0.75"
This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used.
"z_c=1.96"
The rejection region for this two-tailed test is "R=\\{z:|z|>1.96\\}"
The z-statistic is computed as follows:
Since it is observed that "|z|=1.1566<1.96=z_c," it is then concluded that the null hypothesis is not rejected. Therefore, there is not enough evidence to claim that the population proportion "\\bar{p}" is different than "\\pi" at the "\\alpha=0.05" significance level.
The p-value is "p=0.2474," and since "p=0.2474>0.05," it is concluded that the null hypothesis is not rejected. Therefore, there is not enough evidence to claim that the population proportion "\\bar{p}" is different than "\\pi" at the "\\alpha=0.05" significance level.
Which of the following statements is incorrect?
(3) The value of the test statistic is 1.09
(4) The p-value is 0.2502
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