Question

Find the critical value corresponding to an 80% confidence level a recent pull of 1800 people showed that 35% believe gas prices will go down fine point estimate of the proportion of all people who believe gas prices will go down is a sample and equals 500 p equals 0.90 and a 95% confidence level to construct a confidence interval estimate of the population proportion p

Answer 1

I'll answer the pieces you appear to be asking for.

1) Critical value for an 80% confidence level
- z* = 1.2816 (often rounded to 1.28).

2) Sample of n = 1800 with 35% saying gas prices will go down
- Point estimate p̂ = 0.35.
- If you want a 95% CI for this proportion: z* = 1.96.
- SE = sqrt[p̂(1 − p̂)/n] = sqrt(0.35·0.65/1800) ≈ 0.01125
- ME = 1.96·SE ≈ 0.0221
- 95% CI ≈ 0.35 ± 0.0221 = (0.3279, 0.3721) ≈ (32.8%, 37.2%).

3) Sample of n = 500 with p̂ = 0.90 (95% confidence interval)
- Check: np̂ = 450 and n(1−p̂) = 50, both ≥ 5 so normal approx OK.
- SE = sqrt(0.90·0.10/500) = sqrt(0.09/500) ≈ 0.01342
- ME = 1.96·SE ≈ 0.0263
- 95% CI ≈ 0.90 ± 0.0263 = (0.8737, 0.9263) ≈ (87.4%, 92.6%).

If you meant something different by your mixed statement, tell me which sample and confidence level you want and I’ll recompute.