Do men score higher on average compared to women on their statistics finals? Final exam scores of twelve randomly selected male statistics students and ten randomly selected female statistics students are shown below. Male: 65 94 63 85 84 72 79 80 95 79 75 84 Female: 54 60 81 72 65 66 61 77 64 77 Assume both follow a Normal distribution. What can be concluded at the the a = 0.01 level of significance level of significance? For this study, we should use t-test for the difference between two independent population means a. The null and alternative hypotheses would be: Ho: μ1 ♦ μ2 (please enter a decimal) H₁: μ1 μ2 (Please enter a decimal) b. The test statistic t ♦ = 3.125 x (please show your answer to 3 decimal places.) c. The p-value .0028 x (Please show your answer to 4 decimal places.) d. The p-value is α e. Based on this, we should reject + the null hypothesis. f. Thus, the final conclusion is that ... The results are statistically insignificant at a = 0.01, so there is insufficient evidence to conclude that the population mean statistics final exam score for men is more than the population mean statistics final exam score for women. ● The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the population mean statistics final exam score for men is more than the population mean statistics final exam score for women. The results are statistically insignificant at a = 0.01, so there is statistically significant evidence to conclude that the population mean statistics final exam score for men is equal to the population mean statistics final exam score for women. The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the mean final exam score for the twelve men that were observed is more than the mean final exam score for the ten women that were observed.
Do men score higher on average compared to women on their statistics finals? Final exam scores of twelve randomly selected male statistics students and ten randomly selected female statistics students are shown below. Male: 65 94 63 85 84 72 79 80 95 79 75 84 Female: 54 60 81 72 65 66 61 77 64 77 Assume both follow a Normal distribution. What can be concluded at the the a = 0.01 level of significance level of significance? For this study, we should use t-test for the difference between two independent population means a. The null and alternative hypotheses would be: Ho: μ1 ♦ μ2 (please enter a decimal) H₁: μ1 μ2 (Please enter a decimal) b. The test statistic t ♦ = 3.125 x (please show your answer to 3 decimal places.) c. The p-value .0028 x (Please show your answer to 4 decimal places.) d. The p-value is α e. Based on this, we should reject + the null hypothesis. f. Thus, the final conclusion is that ... The results are statistically insignificant at a = 0.01, so there is insufficient evidence to conclude that the population mean statistics final exam score for men is more than the population mean statistics final exam score for women. ● The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the population mean statistics final exam score for men is more than the population mean statistics final exam score for women. The results are statistically insignificant at a = 0.01, so there is statistically significant evidence to conclude that the population mean statistics final exam score for men is equal to the population mean statistics final exam score for women. The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the mean final exam score for the twelve men that were observed is more than the mean final exam score for the ten women that were observed.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:### Do men score higher on average compared to women on their statistics finals?
Final exam scores of twelve randomly selected male statistics students and ten randomly selected female statistics students are shown below.
- **Male:** 65, 94, 63, 85, 84, 72, 79, 80, 95, 79, 75, 84
- **Female:** 54, 60, 81, 72, 65, 66, 61, 77, 64, 77
Assume both follow a Normal distribution. What can be concluded at the the α = 0.01 level of significance?
For this study, we should use **t-test for the difference between two independent population means**.
#### a. The null and alternative hypotheses would be:
- \(H_0\): \(\mu_1 = \mu_2\) (The population mean final exam scores for men and women are equal)
- \(H_1\): \(\mu_1 > \mu_2\) (The population mean final exam score for men is greater than that for women)
#### b. The test statistic \( t \)
\( t \) = 3.125
(The test statistic should be shown to 3 decimal places.)
#### c. The p-value
p-value = 0.0028
(The p-value should be shown to 4 decimal places.)
#### d. The p-value is \( \leq \alpha \)
(Here, α = 0.01)
#### e. Based on this, we should reject the null hypothesis.
#### f. Thus, the final conclusion is that...
The results are statistically significant at α = 0.01, so there is sufficient evidence to conclude that the population mean statistics final exam score for men is more than the population mean statistics final exam score for women.
### Explanation
This study used a two-tailed t-test to compare the final exam scores of male and female statistics students. The hypotheses were structured to test whether male students scored higher on average than female students. Given the test statistic of 3.125 and a p-value of 0.0028, the p-value is less than α (0.01), leading to the rejection of the null hypothesis. Therefore, it can be concluded that, at the 0.01 level of significance, male statistics students score higher on average in
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