Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use the traditional method or P-value method as indicated. 31) 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 $ar{x}_1$ = 12.2 hr $ar{x}_2$ = 14.3 hr $s_1$ = 3.9 hr $s_2$ = 5.2 hr $n_1$ = 14 $n_2$ = 17 Use a 0.05 significance level to test the claim that the mean amount of time 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. Make sure to state Null Hypothesis, Alternative Hypothesis, test score, p value and state conclusion in plain english and in context of the problem.
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Null Hypothesis (H0): The mean amount of time spent watching television by women is equal to the mean amount of time spent watching television by men. Mathematically, this can be represented as: H0: μ1 = μ2 Alternative Hypothesis (H1): The mean amount of time Show more…
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Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Do the following: a. Test the given claim using the Pvalue method or critical value method. b. Construct a confidence interval suitable for testing the given claim. The accompanying table gives results from a study of the words spoken in a day by men and women, and the original data are in Data Set 17 in Appendix B (based on “Are Women Really More Talkative Than Men?” by Mehl, et al., Science, Vol. 317, No. 5834). Use a 0.01 significance level to test the claim that the mean number of words spoken in a day by men is less than that for women. $$\begin{array}{|l|l|} \hline \text { Men } & \text { Women } \\ \hline \mathrm{n} 1=186 & \mathrm{n} 2=210 \\ \hline \mathrm{x}^{-} 1=15,668.5 & \mathrm{x}^{-} 2=16,215.0 \\ \hline \mathrm{s} 1=8632.5 & \mathrm{s} 2=7301.2 \\ \hline \end{array}$$
Inference From Two Samples
Two Means: Independent Samples
Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Do the following: a. Test the given claim using the Pvalue method or critical value method. b. Construct a confidence interval suitable for testing the given claim. We know that the mean weight of men is greater than the mean weight of women, and the mean height of men is greater than the mean height of women. A person's body mass index (BMI) is computed by dividing weight (kg) by the square of height (m). Given below are the BMI statistics for random samples of males and females from Data Set 1 in Appendix B. Use a 0.05 significance level to test the claim that males and females have the same mean BMI. Male BMI n = 40 , x ? = 28.44075 , s = 7.394076 Female BMI n = 40 , x ? = 26.6005 , s = 5.359442
A researcher was interested in comparing the amount of time 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/she had watched during the previous week. The summary statistics are as follows: Women: Sample mean: 12.5 hrs Sample SD: 3.9 hrs Sample size: 14 Men: Sample mean: 14.3 hrs Sample SD: 5.2 hrs Sample size: 17 Use this data to construct a 99% confidence interval for μ₁ - μ₂, the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men. Assume that the two samples are independent simple random samples selected from normally distributed populations with unequal variances. -6.32 hrs < μ₁ - μ₂ < 2.72 hrs -6.31 hrs < μ₁ - μ₂ < 2.71 hrs -6.45 hrs < μ₁ - μ₂ < 2.85 hrs -6.44 hrs < μ₁ - μ₂ < 2.84 hrs
Dominador T.
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