Question

Suppose that we want to estimate the population average price μ for the grapes per pound. Assume that the price per pound follows the normal distribution. (a). If for a random sample of grape prices obtained from 20 different stores, the sample average price X-bar = $ 1.33 with a sample standard deviation (price) s = $ 0.30 then construct a 95 % confidence interval for μ . (5 points) (b). If the average price obtained from 50 different stores is X-bar = $ 1.48 with the standard deviation σ = $ 0.25 then construct a 99 % confidence interval for μ. (5 points) (c ). State the assumptions that you are making in order to construct the confidence intervals in parts (a) and (b). (6 points)

Answer 1

a) At 95% confidence interval the critical value is t^* = 2.093

The 95% confidence interval for is

+/- t^* * s/

= 1.33 +/- 2.093 * 0.3/

= 1.33 +/- 0.14

= 1.19, 1.47

b) At 99% confidence interval the critical is z^* = 2.58

The 99% confidence interval for is

+/- z^* *

= 1.48 +/- 2.58 * 0.25/

= 1.48 +/- 0.09

= 1.39, 1.57

c) The data is a simple random sample.

The sample values are independent of each other.

The sample size is less than or equal to 10% of the population.