Question

Do men score lower on average compared to women on their statistics test? test scores of nineteen randomly selected male statistics students and twenty-eight randomly selected female statistics students are shown below. Assume Equal Variances.

Male:  86, 83, 74, 76, 80, 63, 94, 91, 65, 95, 57, 91, 84, 85, 79, 76, 87, 94, 64

Excel

Female:  88, 99, 82, 90, 65, 99, 76, 93, 93, 69, 70, 89, 96, 83, 74, 77, 90, 91, 100, 78, 76, 100, 78, 84, 100, 72, 100, 103

Excel

Assume both follow a Normal distribution. What can be concluded at the = 0.05 level of the significance?

For this study, we should use Select an answer t-test for the difference between two dependent population means t-test for the difference between two independent population means t-test for a population mean z-test for the difference between two population proportions z-test for a population proportion

1. The null and alternative hypotheses would be:   
2.   

H0:H0:  Select an answer μ1 p1  Select an answer ≠ = ≤ ≥  Select an answer p2 μ2  (please enter a decimal)   

H1:H1:  Select an answer p1 μ1  Select an answer < > ≠ =  Select an answer μ2 p2  (Please enter a decimal)

2. The test statistic ? t z
3. The test statistic = (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer accept fail to reject reject  the null hypothesis.
7. Thus, the conclusion is that ... Select an answer At the 5% significance level, the data provides insufficient evidence to conclude that the population mean statistics test score for men is less than the population mean statistics test score for women. At the 5% significance level, the data provides sufficient evidence to conclude that the population mean statistics test score for men is less than the population mean statistics test score for women.

Answer 1

Answer Date: 30/07/2020 To test the claim is that the population mean statistics test score for men is less than the population mean statistics test score for women at 5% significance level. a) They should used t-test for the difference between two independent population means due to each sample male and female is taken from different populations. b) The null and alternative hypothesis is, H:42 42 H, :μ, < μ a)

The type of test statistics is t used due to the sample size for each sample is small, assume both population normally distribution and the population standard deviation of each sample is unknown. b) The t-test statistics is, By using Excel software, find t-test statistics with the help of following steps: 1) Import the data. 2) Select t-test: Two Sample Assuming Equal Variances from Data Analysis in Data menu. 3) Select Variable 1 Range and Variable 2 Range. 4) Give Hypothesized Mean Difference. 5) Click Labels and enter Alpha. 6) Choose Output Range from Output options. 7) Click Ok.

t-Test: Two-Sample Assuming Equal Variances Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail Male Female 80.21053 86.25 131.1754 127.4537 19 28 128.9424 0 45 -1.7894 0.040141 1.679427 From the Excel output, the t-test statistics is -1.789 The p-value for this test is, From the Excel output in part (b), the p-value for this test is 0.0401

d) Decision The p-value is less than or equal 0.05 which is 0.0401. e) So, the null hypothesis is rejected due to the p-value is less than 0.05 in part (d). f) At 5% level of significance level, the data provides sufficient evidence to conclude that the population mean statistics test score for men is less than the population mean statistics test score for women. The result is statistically significant. The correct answer is 2