The professional organization for private colleges and universities
professors reported that more than 17% of professors attended a
national convention in the past year. To test this claim, a researcher
surveyed 200 professors and found that 45 has attended a national
convention in the past year. At 𝛼 = 0.05, test the claim that this figure
is correct using p -value method.
The following null and alternative hypotheses for the population proportion needs to be tested:
"H_0:p\\le0.17"
"H_1:p>0.17"
This corresponds to a right-tailed test, for which a z-test for one population proportion will be used.
Based on the information provided, the significance level is "\\alpha = 0.05," and the critical value for a right-tailed test is "z_c = 1.6449."
The rejection region for this right-tailed test is "R = \\{z: z > 1.6449\\}."
The z-statistic is computed as follows:
Using the P-value approach: The p-value is "p = P(Z>2.0707)=0.019193," and since "p = 0.019193 < 0.05=\\alpha," it is concluded that the null hypothesis is rejected.
Therefore, there is enough evidence to claim that the population proportion "p" is greater than "0.17," at the "\\alpha = 0.05" significance level.
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