9.1 When would a researcher use a t statistic for his hypothesis test instead of
ID: 3062588 • Letter: 9
Question
9.1 When would a researcher use a t statistic for his hypothesis test instead of a z-score?
9.2 Dr. Froome is interested in whether students prefer to send text messages or traditional emails. In the experiment, students are given 10 messages to send to a person in another room; the researchers record the proportion of times the students use a text message instead of an email. (For example, a student who sends 6 text messages would score 0.6) Assume that population mean is .5. (In other words, there is no preference to use texting vs. emailing)
What would be the null hypothesis in this study? (State the hypothesis using notation and remember to be specific with your prediction)
H0: p = 0.5 H1:
9.3 Dr. Froome obtains the following scores from the students in his study:
X
f
0.4
1
0.5
4
0.6
3
0.7
1
0.8
2
0.9
0
1.0
1
What is the estimated standard error of the mean for this sample?
9.4 What is the t statistic for this sample of students from question 9.3?
9.5 Using a two-tailed test with a p-value of .01, what decision should Dr. Froome make regarding student preferences for text messaging? (write the decision in APA style as it would be reported in a paper)
9.6 Would Dr. Froome’s conclusion be different if he’d used = .05? Why or Why not?
9.7 Calculate the effect size for Dr. Froome’s study. Use estimated d
9.8 Calculate the effect size for Dr. Froome’s study. Use r2
9.9 Using r2 as the effect size, would you describe this effect as being small, medium or large?
9.10 Calculate the 95% CI associated with Dr. Froome’s study
X
f
0.4
1
0.5
4
0.6
3
0.7
1
0.8
2
0.9
0
1.0
1
Explanation / Answer
Solution-
1. We use t statistc instead of Z score in the following situation-
When we don't know the value of population variance and sample size is also small.
Thanks!
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