Question

The manager of a paint supply store wants to estimate the actual amount of paint contained in 1​-gallon cans purchased from a nationally known manufacturer. The​ manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.01 gallon. A random sample of 50 cans is​ selected, and the sample mean amount of paint per 1​-gallon can is 0.996 gallon. Complete parts​ (a) through​ (d). a. Construct a 95​% confidence interval estimate for the population mean amount of paint included in a​ 1-gallon can. 0.99323less than or equalsmuless than or equals 0.99877 ​(Round to five decimal places as​ needed.)

b. On the basis of these​ results, do you think the manager has a right to complain to the​ manufacturer? Why? d. Construct a 90​% confidence interval estimate. How does this change your answer to part​ (b)?

nothingless than or equalsmuless than or equals nothing ​(Round to five decimal places as​ needed.)

Answer 1

a) At 95% confidence interval the critical value is z^* = 1.96

The 95% confidence interval is

+/- z^* *

= 0.996 +/- 1.96 * 0.01/

= 0.996 +/- 0.00277

= 0.99323, 0.99877

b) Since 1, does not lie in the interval, so the manufacturer has a right to complain to the manufacturer.

c) At 90% confidence interval the critical value is z^* = 1.645

The 90% confidence interval is

+/- z^* *

= 0.996 +/- 1.645 * 0.01/

= 0.996 +/- 0.00233

= 0.99367, 0.99833

It doesn't change the answer to part - b. Because the interval doesn't contain 1.