In: Statistics and Probability
Elderly drivers. A polling agency interviews 754 American adults and finds that 467 think licensed drivers should be required to retake their road test once they reach 65 years of age. Round all answers to 4 decimal places.
1. Calculate the point estimate for the proportion of American adults that think licensed drivers should be required to retake their road test once they reach 65 years of age.
2. Calculate the standard error for the point estimate you calculated in part 1.
3. Calculate the margin of error for a 99% confidence interval for the proportion of American adults that think licensed drivers should be required to retake their road test once they reach 65 years of age.
4. What are the lower and upper limits for the 99% confidence interval? ( , )
5. Use the information from the polling agency to determine the sample size needed to construct a 99% confidence interval with a margin of error of no more than 5%. For consistency, use the reported sample proportion for the planning value of p* (rounded to 4 decimal places) and round your Z* value to 3 decimal places. Your answer should be an integer.
a)
sample proportion, = 0.6194
b)
sample size, n = 754
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.6194 * (1 - 0.6194)/754) = 0.0177
c)
Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.576
Margin of Error, ME = zc * SE
ME = 2.576 * 0.0177
ME = 0.0456
d)
CI = (pcap - z*SE, pcap + z*SE)
CI = (0.6194 - 2.576 * 0.0177 , 0.6194 + 2.576 * 0.0177)
CI = (0.5738 , 0.6650)
5)
The following information is provided,
Significance Level, α = 0.01, Margin of Error, E = 0.05
The provided estimate of proportion p is, p = 0.6194
The critical value for significance level, α = 0.01 is 2.576.
The following formula is used to compute the minimum sample size
required to estimate the population proportion p within the
required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.6194*(1 - 0.6194)*(2.576/0.05)^2
n = 625.74
Therefore, the sample size needed to satisfy the condition n
>= 625.74 and it must be an integer number, we conclude that the
minimum required sample size is n = 626
Ans : Sample size, n = 626