Question

1A. A soft drink manufacturer wishes to know how many soft drinks adults drink each week. They want to construct a 95% confidence interval with an error of no more than 0.07. A consultant has informed them that a previous study found the mean to be 3.7 soft drinks per week and found the variance to be 1.21. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.

1B.

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.0pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 180 engines and the mean pressure was 5.1 pounds/square inch. Assume the standard deviation is known to be 0.6. A level of significance of 0.1 will be used. Determine the decision rule.

Answer 1

A) At 95% confidence level, the critical value is z_0.025 = 1.96

Margin of error = 0.07

or, z_0.025 * = 0.07

or, 1.96 * 1.1/ = 0.07

or, n = ((1.96 * 1.1)/0.07)^2

or, n = 949

B) H₀: = 5

     H₁: > 5

The test statistic is

   

  

At 0.1 significance level, the critical value is z_0.9 = 1.28

Reject H₀, if z > 1.28

Since the test statistic value is greater than the critical value, so reject H₀.