Question

On each of the following 1- State the null and alternte hypothesis. 2- Show the test statistic, 3- State the conclusion in terns of the null hypothesis, 4-State the conclusion in terms of the question 5-tell the p-value (if one sided):

Emma dosent believe that women take longer in the restroom than men, so she stands outside the restrooms in the union and times people as they enter and exit. Besides getting strange looks, she collects the following data. The mean time for 30 men was 4 minutes with a standard deviation of 2, while the mean of 20 women was 5 minutes with a standard deviation of 3. Is the mean significantly higher for women than men at a 5% level of significance.

Answer 1

Solution:-

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

Null hypothesis: u₁> u₂
Alternative hypothesis: u₁ < u₂

Note that these hypotheses constitute a one-tailed test.

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 of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 0.76376
DF = 48

t = [ (x₁ - x₂) - d ] / SE

t = - 1.31

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 -1.31

Therefore, the P-value in this analysis is 0.098.

Interpret results. Since the P-value (0.098) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that mean significantly higher for women than men.