Question

Please, complete the following exercises:

1. A Quality Control inspector wants to estimate the true population mean for the diameter of an extruded plastic rod. She samples 65 rods. The mean diameter is 2.18 inches. From previous work, the population standard deviation is known to be 0.2 inches. Find a 95% confidence interval for the true mean diameter of all plastic rods.

2.You work in Human Resources at Merrill Lynch. You plan to survey employees to find their average medical expenses. You want to be 95% confident that the sample mean is within ± $60.  A pilot study showed that Sx was about $420. What sample size do you use?

3.You’re a Q/C inspector for Gallo. The s for 2-liter bottles is .05 liters. A random sample of 100 bottles showed x = 1.98 liters. What is the 95% confidence interval estimate of the true mean amount in 2-liter bottles?

4. You’re a time study analyst in manufacturing. You’ve recorded the following task times (min.):
3.5, 4.3, 4.1, 3.7, 3.9, 3.2. What is the 90% confidence interval estimate of the population mean task time?

5. You’re a production manager for a newspaper. You want to find the % defective. Of 250 newspapers, 50 had defects. What is the 95% confidence interval estimate of the population proportion defective?

Answer 1

Let x be the diameter of an extruded plastic rod.

Sample size ( n) = 65

Sample mean ( ) = 2.18 inches

Population standard deviation ( σ ) = 0.2 inches

Confidence level = 95%

Therefore α = 1 - 0.95 = 0.05

α/2 = 0.025

Using z table,

Value of z corresponding to area 0.025 is z = 1.96

Confidence interval =

Confidence interval =

Confidence interval =

Lower bound = 2.18 - 0.0486

Lower bound = 2.1314

Upper bound = 2.18 + 0.0486

Upper bound = 2.2286

Therefore 95% confidence interval is

( 2.1314 , 2.2286 )