2. In 2012, 32% had a college degree. A Sociologist has hypothesized that the GS
ID: 3062952 • Letter: 2
Question
2. In 2012, 32% had a college degree. A Sociologist has hypothesized that the GSS sample has a significantly lower proportion with college degree. Is she right? Set a muTakean uoutnthe dsrih b. The null and alternate hypotheses. c. Establish the critical regions. d. Compute the test statistic. e. Make a decision and conclusion. 3. In 2012, the population had 12 years of education. Compare this population mean to a random sample ( 1% of the GSS sample). Is the difference significant? Set alpha-05. In your answer include: (Hint draw a random sample first and then do Descriptiv obtain mean) pie es to a. The null and alternate hypotheses b. Establish the critical regions c. Compute the test statistic. d. Make a decision and conclusion.Explanation / Answer
Solution:-
x = 205 + 354
n = 1974
p = 559/1974
p = 0.2832
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.32
Alternative hypothesis: P < 0.32
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 0.10. 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 ]
= 0.01050
z = (p - P) /
z = - 3.51
zcritical = - 1.645
Rejection region is z less than - 1.645
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 -3.51.
Thus, the P-value = 0.0002
Interpret results. Since the P-value (0.0002) is less than the significance level (0.10), we cannot accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that GSS sample has significantly lower proportion with college graduates.
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