Question

Do men score lower on average compared to women on their statistics test? Test scores of thirteen randomly selected male statistics students and twelve randomly selected female statistics students are shown below.

Male:  84 80 91 86 78 80 69 93 64 81 75 95 63

Female:  92 76 99 73 80 99 70 95 97 95 94 74

Assume both follow a Normal distribution. What can be concluded at the the αα = 0.05 level of significance level of 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 z-test for a population proportion t-test for a population mean z-test for the difference between two population proportions

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

H0:H0:  Select an answer μ1 p1  Select an answer > = ≠ <  Select an answer μ2 p2  (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 ? z t  =  (please show your answer to 3 decimal places.)
3. The p-value =  (Please show your answer to 4 decimal places.)
4. The p-value is ? > ≤  αα
5. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population mean statistics final score for men is less than the population mean statistics final score for women.
   • The results are statistically insignificant at αα = 0.05, so there is statistically significant evidence to conclude that the population mean statistics final score for men is equal to the population mean statistics final score for women.
   • The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the mean final score for the thirteen men that were observed is less than the mean final score for the twelve women that were observed.
   • The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population mean statistics final score for men is less than the population mean statistics final score for women.

Answer 1

For Male :

∑x = 1039

∑x² = 84303

n1 = 13

Mean , x̅1 = Ʃx/n = 1039/13 = 79.9231

Standard deviation, s1 = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(84303-(1039)²/13)/(13-1)] = 10.2588

For Female :

∑x = 1044

∑x² = 92242

n2 = 12

Mean , x̅2 = Ʃx/n = 1044/12 = 87.0000

Standard deviation, s2 = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(92242-(1044)²/12)/(12-1)] = 11.3378

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For this study, we should use t-test for the difference between two independent population means

Null and Alternative hypothesis:

Ho : µ1 = µ2

H1 : µ1 < µ2

Pooled variance :

S²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2) = ((13-1)*10.2588² + (12-1)*11.3378²) / (13+12-2) = 116.3880

Test statistic:

t = (x̅1 - x̅2) / √(s²p(1/n1 + 1/n2 ) = (79.9231 - 87) / √(116.388*(1/13 + 1/12)) = -1.639

df = n1+n2-2 = 23

p-value = T.DIST(-1.6386, 23, 1) = 0.0574

Decision:

p-value > α, Fail to reject the null hypothesis

Conclusion:

The results are statistically insignificant at α = 0.05, so there is insufficient evidence to conclude that the population mean statistics final score for men is less than the population mean statistics final score for women.