Question

a) A researcher wants to test if boys spend more time playing sports on average than girls. Data is collected, resulting in the table below. It is known that the times for sports have a normal distribution in general.

Group	n	Average number of hours	SD
Boy	35	5.2	3.3
Girl	25	3.5	5

Compute the test statistic that is corresponding to the test in the question 9.

Round your answer to two decimal digits.

b)

Let the significance level be 0.05.

Can we reject the null hypothesis?

If we can, choose TRUE, and if not, choose FALSE

Answer 1

For boys:

For girls:

Null and Alternative Hypotheses :

Critical value :

At =0.05 and df =35+25-2 =58, the critical value for this right-tailed test is t_c = 1.67

Test Statistics :

Decision about the null hypothesis :

Since it is observed that t = 1.59 < t_c = 1.67, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = 0.0586, and since p = 0.0586 > 0.05, it is concluded that the null hypothesis is not rejected.

Conclusion :

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that boys spend more time playing sports on average than girls, at the 0.05 significance level.

FALSE, we cant reject null hypothesia at0.05 significance level.