Two random samples of 40 students were drawn independently from two populations of students. assume their aptitude tests are normally distributed and assume the variances of each sample are equal. the following statistics regarding their scores in an aptitude test were obtained: x with bar on top subscript 1 equals 76 comma space s subscript 1 equals 8 comma space x with bar on top subscript 2 equals 73 comma space s subscript 2 equals 7. test at the 5% significance level to determine whether we can infer that the two population means differ. what is the conclusion from your test? a. none of these answers are correct b. do not reject the null hypothesis c. do not accept the null hypothesis d. accept the alternate hypothesis e. reject the null hypothesis

b. Do not reject the null hypothesis

Step-by-step explanation:

Given that two random samples of 40 students were drawn independently from two populations of students.  Assuming equal variances

we have the following data.

Sample 1

Mean:  

76

Standard deviation:  

8

Sample size:  

40

Sample 2

Mean:  

73

Standard deviation:  

7

Sample size:  

40

Difference-3.000

Standard error1.681

95% CI-6.3462 to 0.3462

t-statistic  -1.785

DF  78

Significance levelP = 0.0782

Since p value >0.05,

b. Do not reject the null hypothesis

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%