Question

1. Find the critical value zα/2 that corresponds to a 94% confidence level. Round your answer to two decimal places.

2. The following confidence interval is obtained for a population proportion, p: 0.273 < p < 0.592. Use these confidence interval limits to find the sample proportion . Round your answer to three decimal places. 0.433

3. Find the minimum sample size : How many commuters must be randomly selected to estimate the mean driving time μ of Chicago commuters? We want 99% confidence that the sample mean is within 4.7 minutes of the population mean, and the population standard deviation is known to be 13.7 minutes. 57

Answer 1

Answer:

1.

Given,

The critical value Z(alpha/2) that corresponds to 94% confidence interval is 1.88

2.

CI = 0.273 < p < 0.592

So now we have to compare it with p^ +/- E,

i.e.,

p^ - E = 0.273 --------> (1)

p^ + E = 0.592 ---------> (2)

Adding of two, we get 2p^ = 0.865

p^ = 0.865/2

p^ = 0.4325

substitute p^ in (2)

0.4325 - E = 0.273

E = 0.4325 - 0.273

E = 0.1595

So the confidence interval can be expressed as 0.4325 +/- 0.1595

3.

Given,

CI = 99%

Margin of error E = 4.7

Standard deviation = 13.7

n >= (z*s/E)^2

substitute values

= (2.58*13.7 / 4.7)^2

= 56.56

= 57

So sample size n = 57