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Answer:
We conclude that we fail to reject as there is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.
Step-by-step explanation:
We are given that among 317 tested subjects, results from 25 subjects were wrong.
We have to test the claim that less than 10 percent of the test results are wrong.
<u><em>Let p = proportion of subjects that were wrong.</em></u>
So, Null Hypothesis, : p = 10% {means that 10 percent of the test results are wrong}
Alternate Hypothesis, : p < 10% {means that less than 10 percent of the test results are wrong}
The test statistics that would be used here <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of test results that were wrong =
= 0.08
n = sample of tested subjects = 317
So, <u><em>test statistics</em></u> =
= -1.31
The value of z test statistics is -1.31.
Now, the P-value of the test statistics is given by the following formula;
P-value = P(Z < -1.31) = 1 - P(Z 1.31)
= 1 - 0.9049 = <u>0.095</u>
<u><em>Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.</em></u><em> Since our test statistics is more than the critical value of z as -1.31 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><em><u>we fail to reject our null hypothesis</u></em><em>.</em>
Therefore, we conclude that we fail to reject as there is not sufficient evidence to warrant support of the claim that less than 10 percent of the test results are wrong.