Question

Do women feel differently from men when it comes to tax rates? One question on a survey of randomly selected adults asked, "What percent of income do you believe individuals should pay in income tax?" Complete parts a) through c). Click the icon to view the survey results. a) Draw side-by-side boxplots of tax rates by gender. Choose the correct graph below. Survey Results OA. ОВ. A 10 20 30 40 10 20 30 40 M Oc OD 40 40 Does there appear to be a difference in the income tax rates between genders? O A. No but the maximum income tax rate for males is higher than the maximum income tax rate for females. O B. No because the income tax rate is about the same for males and females. O C. Yes because the income tax rate for males appears have higher median than the income tax rate for females. OD. Yes because the income tax rate for females appears to have a higher median than the income tax rate for males. Gender Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Female Fen Female Female Female Female Female Female Female Female Tax Rate 10 10 6 19 21 15 10 15 3 5 23 10 0 22 10 0 8 20 14 13 20 15 9 17 5 16 15 5 16 25 Gender Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Male Tax Rate 15 20 8 10 17 2 1 15 3 9 15 5 16 35 10 15 2 0 4 5 15 6 10 6 10 24 15 17 8 10 b) Explain why a hypothesis test may be used to test whether the mean tax rates for the two genders differ. Select all that apply. A. Each sample has the same sample size. B. Each sample size is large. OC. Each sample is obtained independently of the other. D. Each sample is a simple random sample. E. Each sample size is small relative to the size of its population. c) Test whether the mean tax rate for females differs from that of males at the a= 0.01 level of significance. Print Done Determine the null and alternative hypotheses for this test. Let Him represent the mean income tax rate for males and let HF represent the mean income tax rate for females. Ho: versus H: 7 7 Find to, the test statistic for this hypothesis test. to-(Round to two decimal places as needed.) Determine the P-value for this test. P-value = (Round to three decimal places as needed.) Click to select your answer(s).

Answer 1

Solution:

36 2 26 24 22 30 28 20 26 18 24 22 16 20- 14- 16 12 14 10- 12 8 10 8 6 6 4 2 M F

The provided sample means are shown below: X = 12.57 X = 10.93 Also, the provided sample standard deviations are: 8 = 6.78 82 = 7.57 and the sample sizes are n = 30 and no = 30. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: HO: Hi = 12 Ha: Hly * Ho This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.01, and the degrees of freedom are df = 58. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal: Hence, it is found that the critical value for this two-tailed test is t = 2.663, for a = 0.01 and df = 58. The rejection region for this two-tailed test is R = {t: t > 2.663). (3) Test Statistics Since it is assumed that the population variances are equal, the t-statistic is computed as follows: t = X1 - 2 (11-1.7+(12-1) (+1) 1, 12-2 V = 0.884 12.57 10.93 (30-1)6.782 +(30-1)7.572 30+30 - 2 (30 + ) V (4) Decision about the null hypothesis Since it is observed that t = 0.884 < t = 2.663, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.3804, and since p = 0.3804 > 0.01, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean Mi is different than je, at the 0.01 significance level.