Section 9.2 1. The proportion of adults living in Stoney Creek who are college g

Question

Section 9.2 1. The proportion of adults living in Stoney Creek who are college graduates is estimated to be p 0.3. To test this hypothesis, a random sample of 60 adults is selected. If the number of college graduates in our sample is anywhere from 12 to 24, we shall accept the null hypothesis that p 0.3; otherwise, we shall conclude that p 0.3. Evaluate a, assuming that p 0.3. Evaluate ? for the alternatives P=0.2 and p=0.4. Is this a good test procedure? 2. Repeat Exercise 1 when n 200 and the acceptance region is defined to be 48 S x S 72, where x represents the number of college graduates in our sample.

Explanation / Answer

Solution:-

17)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: ? = 8
Alternative hypothesis: ? ? 8

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.5052

DF = n - 1

D.F = 11
t = (x - ?) / SE

t = 1.78

where s is the standard deviation of the sample, x is the sample mean, ? is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 11 degrees of freedom is less than -1.78 or greater than 1.78.

Thus, the P-value = 0.103

Interpret results. Since the P-value (0.103) is greater than the significance level (0.01), we cannot reject the null hypothesis.

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