Suppose the coach of the football team wants to estimate the proportion of the p
ID: 3385463 • Letter: S
Question
Suppose the coach of the football team wants to estimate the proportion of the population of fans who support his current starter lineup. The coach wants the estimate to be .04 of the true proportion. Assume a 90 percent level of confidence. The coach estimated the proportion supporting the current starter lineup to be .60.
1. Construct a 90% confidence interval using a sample size of 50, then of 100, then of 1,000.
2. How did changing the sample size affect the size of the interval?
3. What is the error of the estimate for each of these sample sizes?
4. How large of a sample is required for the error of the estimate to be within +.04 of the population proportion?
5. How large would the sample have to be if the coach of the team were not available?
(I just need help with questions 4 and 5. Please include TI-84 steps thanks.)
Explanation / Answer
Hi! Unfortunately, there's no special function for a ti-84 that would estimate sample sizes.
So, we really have to do it manually using formulas.
4.
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.05
Using a table/technology,
z(alpha/2) = 1.644853627
Also,
E = 0.04
p = 0.6
Thus,
n = 405.8315181
Rounding up,
n = 406 [ANSWER]
******************
5.
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.05
As there is no previous estimate for p, we set p = 0.5.
Using a table/technology,
z(alpha/2) = 1.644853627
Also,
E = 0.04
p = 0.5
Thus,
n = 422.7411647
Rounding up,
n = 423 [ANSWER]
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