We are interested in studying the relationship satisfaction of young adults befo

Question

We are interested in studying the relationship satisfaction of young adults before and after they go off to college and are separated from their significant other. A random sample of 35 young adults who are about to be separated from their significant other by going to college was collected. Each participant was asked a series of questions, which was then converted to a satisfaction score ranging from 0-50 points (a higher score indicates greater satisfaction). The satisfaction score for each participant was measured before leaving for college and after spending the first semester at college away from their significant other. For each participant, the difference in satisfaction score was computed (satisfaction score after minus satisfaction score before). The 90% confidence interval for the population mean difference in satisfaction score for all such young adults who are separated from their significant other after one semester of college is given by: -9.0 points to -0.9 points.

a) Based on the provided 90% confidence interval, do the data support that the population mean satisfaction score significantly changed after going off to college for the population of all such young adults (at the 10% significance level)? State your answer of Yes or No and provide a brief explanation in context.

b) Is the following statement True or False? About 90% of all such young adults who separate from their significant other to attend college will have a decrease in satisfaction score between 0.9 and 9.0 points.

c) Is the following statement True or False? If this study were repeated many times, with random samples of 35 young adults who separate from their significant other, and for each sample a corresponding 90% confidence interval was made, 90% of the resulting intervals are expected to contain the sample mean difference in satisfaction score.

d) Is the following statement True or False? The Central Limit Theorem states that since the sample is large enough (larger than 25 or 30), then we can conclude that the difference in satisfaction scores (difference = After - Before) for the population of all such young adults follows approximately a normal distribution.

Explanation / Answer

a)

As the whole interval is negative, then:

YES, there is significant decrease in satisfaction scores for each participant before leaving for college and after spending the first semester at college away from their significant other.

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B)

FALSE. The confidence level talks about how confident we are that the interval "catches" the true mean.

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c)

TRUE.

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d)

As the sample size requirements are satisfied, then TRUE. [ANSWER]

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