Question

7. P(z<1.34) (four decimal places)

8. Candidate only wants a 2.5% margin error at a 97.5% confidence level, what size of sample is needed?

9. Estimate this proportion to within 4% at the 95% confidence level, how many randomly selected college students must we survey?

10. 420 people were asked if they like dogs, 22% said they did. Find the margin of error for the poll at 95% confidence level. (four decimals

Answer 1

7)

Here, μ = 0, σ = 1 and x = 1.34. We need to compute P(X <= 1.34). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (1.34 - 0)/1 = 1.34

Therefore,
P(X <= 1.34) = P(z <= (1.34 - 0)/1)
= P(z <= 1.34)
= 0.9099

8)

The following information is provided,
Significance Level, α = 0.025, Margin of Error, E = 0.025

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.025 is 2.24.

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 = 0.5*(1 - 0.5)*(2.24/0.025)^2
n = 2007.04

Therefore, the sample size needed to satisfy the condition n >= 2007.04 and it must be an integer number, we conclude that the minimum required sample size is n = 2008
Ans : Sample size, n = 2008 or 2007

9)

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.04

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.05 is 1.96.

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 = 0.5*(1 - 0.5)*(1.96/0.04)^2
n = 600.25

Therefore, the sample size needed to satisfy the condition n >= 600.25 and it must be an integer number, we conclude that the minimum required sample size is n = 601
Ans : Sample size, n = 601 or 600

10)

sample proportion, = 0.22
sample size, n = 420
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.22 * (1 - 0.22)/420) = 0.0202

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0202
ME = 0.0396