A researcher was interested in comparing the amount of time (in hours) spent wat
ID: 3315743 • Letter: A
Question
A researcher was interested in comparing the amount of time (in hours) spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows. Women Men x1 12.5 hr x2 13.8 hr sl = 3.9 hr s2 = 5.2 hr nl-14 n2 -17 Use a 0.05 significance level to test the claim that the mean amount of time 7. spent watching television by women is smaller than the mean amount of time spent watching television by men. Use the traditional method of hypothesis testing.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Women< Men
Alternative hypothesis: Women > Men
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 of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 1.636
DF = 29
t = [ (x1 - x2) - d ] / SE
t = - 0.795
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 (10) produced a t statistic of - 0.795. We use the t Distribution Calculator to find P(t < - 0.795).
Therefore, the P-value in this analysis is 0.22.
Interpret results. Since the P-value (0.22) is greater than the significance level (0.05), we cannot reject the null hypothesis.
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