A. A rural studies scholar is interested in studying how “connected” are the peo

Question

A. A rural studies scholar is interested in studying how “connected” are the people in a small town. He can’t talk to all 1,000 people, but he does have a randomly drawn sample of 120 people who tell him how many different organizations they are a part of. The mean for this sample is 3.1, and the standard deviation is 1.1. His goal is to be able to say, “I’m 95% sure that the mean number of organizations that residents belong to is between ___ and ___.” What is the standard error that he needs to compute to move forward with his data analysis?

B. Assume that the answer to the previous question is .10. What is the margin of error he will next compute, recalling that he wishes to make his claim at the 95% level of confidence? Pick the answer that is closest to what you compute.

c. Using the margin of error calculated in the previous question (the rounded value), what is the confidence interval (i.e. the numbers that would go into the blanks) that describes the average number of organizations that residents are a part of (at the 95% level of confidence)?

Explanation / Answer

Result:

A. A rural studies scholar is interested in studying how “connected” are the people in a small town. He can’t talk to all 1,000 people, but he does have a randomly drawn sample of 120 people who tell him how many different organizations they are a part of. The mean for this sample is 3.1, and the standard deviation is 1.1. His goal is to be able to say, “I’m 95% sure that the mean number of organizations that residents belong to is between ___ and ___.” What is the standard error that he needs to compute to move forward with his data analysis?

standard error = sd/sqrt(n) = 1.1/sqrt(120) =0.100416

since sample size is more than 5% of the population size, finite population correction to be used.

standard error = sd/sqrt(n) *(sqrt[ (N-n)/(N-1)]

standard error = 0.100416*sqrt(880/999) =0.094246

B. Assume that the answer to the previous question is .10. What is the margin of error he will next compute, recalling that he wishes to make his claim at the 95% level of confidence? Pick the answer that is closest to what you compute.

t value for 95% level with 119 df = 1.98

margin of error = 1.98*0.10 = 0.198

c. Using the margin of error calculated in the previous question (the rounded value), what is the confidence interval (i.e. the numbers that would go into the blanks) that describes the average number of organizations that residents are a part of (at the 95% level of confidence)?

Lower limit = 3.1-0.198 = 2.902

upper limit = 3.1+0.198 = 3.298

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