A social scientist is interested in determining how many hours per week Pony Clu

Question

A social scientist is interested in determining how many hours per week Pony Club youth spend with their horses. His survey results indicate that s = 12.5 hrs.

a. How many youth are needed to estimate the number of hours spent per week with the horse within 2 hr with 95% confidence?

b. How about within 2 hr with 90% confidence?

c. How about within 1 hr with 95% confidence?

d. How about within 1 hr with 90% confidence?

e. Based on your results above, what can you say about the effect of required accuracy and confidence on sample size estimates?

This is all the information given for the question.

Explanation / Answer

here std deviation s=12.5

a) for 90% Ci, Z=1.64485

margin of error E =2

sample size =(Z*s/E)2 =~106 rounding it up

b) for 95% CI, z=1.96

E=1

sample size =(Z*s/E)2 = ~601

c) z=1.64485

E=1

sample size =(Z*s/E)2 =~423

e) as margin of error decreases or confidence interval increases ; sample size requirement increases

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