Question

Do men score lower on average compared to women on their statistics finals? Final exam scores of twelve randomly selected male statistics students and twelve randomly selected female statistics students are shown below. Male: 74 62 81 68 82 77 85 61 67 87 66 83 Female: 959973 78 92 84 82 78 81 90 78 67 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 Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer D P D Select an answer H: Select an answer ? Select an answer b. The test statistic ? D (please show your answer to 2 decimal places.) c. The p-value (Please show your answer to 4 decimal places.) d. The p-value is ? Da e. Based on this, we should select an answer the null hypothesis. f. Thus, the final conclusion is that ... The results are statistically significant at a =0.01, so there is sufficient evidence to conclude that the mean final exam score for the

Answer 1

we will use t test for two independent samples

Ho :   µ1 - µ2 =   0 or µ1 =µ2
Ha :   µ1-µ2 <   0 or µ1<µ2

Sample #1   ---->   1
mean of sample 1,    x̅1=   74.417
standard deviation of sample 1,   s1 =    9.307
size of sample 1,    n1=   12
      
Sample #2   ---->   2
mean of sample 2,    x̅2=   83.083
standard deviation of sample 2,   s2 =    9.376
size of sample 2,    n2=   12

b)

difference in sample means =    x̅1-x̅2 =    74.4167   -   83.1   =   -8.667  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    9.3416                  
std error , SE =    Sp*√(1/n1+1/n2) =    3.8137                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -8.6667   -   0   ) /    3.81   =   -2.27

c)

Degree of freedom, DF=   n1+n2-2 =    22  
p-value =        0.0166 [ excel function: =T.DIST(t stat,df) ]

d)

p value is greater than α

e) should not reject

f) the result are not statiscally significant....,so there is not sufficient evidence...............