Assume that a simple random sample has been selected and test the given claim. U

Question

Assume that a simple random sample has been selected and test the given claim. Use Minitab to conduct the following hypothesis test. Identify the null and alternative hypotheses, test statistic. P-value, and state the final conclusion that addresses the original claim. The ages of actresses when they won an acting award is summarized by the statistics n = 83, x bar = 35.0 years, and s = 11.1 years. Use a 0.05 significance level to test the claim that the mean age of actresses when they win an acting award differs from 34 years. What are the hypotheses? A. H_0: mu = 34 years H_1: mu greaterthanorequalto 34 years B. H_0: mu notequalto 34 years H_1: mu = 34 years C. H_0: mu = 34 years H_1: mu notequalto 34 years D. H_0: mu = 34 years H_1:

Explanation / Answer

Solution:-

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

Null hypothesis: = 34

Alternative hypothesis: 34

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 0.05. 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 = 1.218

DF = n - 1 = 83 - 1

D.F = 82

t = (x - ) / SE

t = 1.56

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 82 degrees of freedom is less than -1.56 or greater than 1.56

Thus, the P-value = 0.1226

Interpret results. Since the P-value (0.1226) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the mean age of the actrersses when they win an acting award is 34 years.

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