A sociologist believes that for people under the age of 30, women sleep longer p

Question

A sociologist believes that for people under the age of 30, women sleep longer per night on the weekend than men. 24 people were surveyed. Test at alpha =5%. The following summary statistics were determined from the sample.

a) State the Null and Alternate Hypothesis in symbols and in words.

b) Calculate the expected results for the hypothesis test sampling distribution, assuming the Null Hypothesis is true. (i.e., name and graph of the sampling distribution, mean and standard error)

c) Identify the standard distribution that best approximates the sampling distribution. d) Formulate the decision rule(you can use either critical test scores or p-values)

e) Determine the statistical sample results, i.e., the differences between the sample means, the pooled standard deviations, the standard error, the test statistic and p-value.

f) Determine the conclusion in terms of the Null and Alternate Hypotheses. Do the sample results indicate that the sociologist’s claim is supported at alpha= 5%?

Explanation / Answer

Solution:-

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

Null hypothesis: Men> Women
Alternative hypothesis: Men < Women

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

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

SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.9763

DF = 22

t = [ (x1 - x2) - d ] / SE

t = - 0.133

where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of - 0.133. We use the t Distribution Calculator to find P(t < - 0.133)

Therefore, the P-value in this analysis is 0.448

Interpret results. Since the P-value (0.448) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Hence from the above test we do not have sufficient evidence in the favor of the claim that for people under the age of 30, women sleep longer per night on the weekend than men.

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