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A group of students wanted to investigate the claim that the average number of text messages sent yesterday by

students in their school was greater than 100. They asked each student in a random sample of 50 students how many

text messages he or she sent yesterday. An appropriate t-test was conducted and resulted in a p-value of 0.0853.

Assuming the conditions for the t-test were met, which of the following is an appropriate conclusion?


(A) Because p .  0 10 , at the 10% significance level, it can be concluded that the mean number of text messages sent

yesterday by students in the school is less than 100.



(B) Because p .  0 10 , at the 10% significance level, it cannot be concluded that the mean number of text messages

sent yesterday by students in the school is greater than 100.



(C) Because p .  0 05 , at the 5% significance level, it can be concluded that the mean number of text messages sent

yesterday by students in the school is greater than 100.



(D) Because p .  0 05 , at the 5% significance level, it can be concluded that the mean number of text messages sent

yesterday by students in the school is less than 100.



(E) Because p .  0 05 , at the 5% significance level, it cannot be concluded that the mean number of text messages

sent yesterday by students in the school is greater than 100.

Respuesta :

First we need to write the null and alternate hypothesis for this case.

Let x be the average number of text message sent. Then

Null hypothesis: x = 100
Alternate hypothesis: x > 100

The p value is 0.0853

If p value > significance level, then the null hypothesis is not rejected. If p value < significance level, then the null hypothesis is rejected.

If significance level is 10%(0.10), the p value will be less than 0.10 and we reject the null hypothesis and CAN conclude that:
The mean number of text messages sent yesterday was greater than 100.

If significance level is 5%(0.05), the p value will be greater than 0.05 and we cannot reject the null hypothesis and CANNOT conclude that:
The mean number of text messages sent yesterday was greater than 100.

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