Question

QUESTION 22

1. Emily does her research project on this question: On a scale of 1 to 10, how happy are you with your life right now? (1 = completely unhappy; 10 = completely happy). She predicts her Facebook Friends will provide a mean of 6 in their response. After gathering data from 30 friends, she gets a sample mean of 5.1 with a standard deviation of 2.8.

Was her guess reasonable? Assume 95% confidence. (Hint: You may use either a confidence interval or hypothesis test to help you answer this question.)

P.S. Credit to an RCSJ student this semester for this research question. Very creative and thought-provoking question and her reserach project and results were quite interesting!

	A.	Yes, her guess was reasonable.
	B.	No, her guess was not reasonable.

Answer 1

Step 1:

Ho: = 6

Ha: 6

Null hypohesis states that mean response of survey is 6

Alternative hypohesis states that mean response of survey is not equal to 6

Step 2

n = 30

sample mean = 5.1

sample sd = 2.8

Assuming data is normally distributed and also as the population sd is not given, we will calculte t stat

Step 3:

df = 29, level of sgnificane = 0.05

t-value (two-tailed) = +/- 2.045

As the t stat (-1.761) does not fall in the rejection area, we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that mean response of survey is not equal to 6.

Yes, her guess was reasonable.