Economists often track employment trends by measuring the proportion of people w
ID: 3060673 • Letter: E
Question
Economists often track employment trends by measuring the proportion of people who are oyed," meaning they are either unemployed or would like to work full time but are only n the summer of 2013, 17.6% of Americans were "underemployed." underempl orking part-time. I mayor of Thicksburg wants to show the voters that the situation is not as bad in his town as it is in thae vest of the country. Hlis staff takes a simple randon sample of 300 Thicsburg residents and finds that 45 of them are underemployed The (a) Do the data give convincing evidence that the proportion of underemployed in Thicksburg is lower than elsewhere in the country? Support your answer with a significance testExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.176
Alternative hypothesis: P < 0.176
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.02199
z = (p - P) /
z = - 1.18
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than -1.18.
Thus, the P-value = 0.119.
Interpret results. Since the P-value (0.119) is more than the significance level (0.05), we have to accept the null hypothesis.
From the above test we do not have the sufficient evidence that the proportion of underemployed in Thicksburg is lower than elsewhere in the country.
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