manufacturer produces piston rings for automobile engine It

manufacturer produces piston rings for automobile engine. It is known that ring diameter is normall stributed with a sigma = 1 millimeters. A random sample of 25 rings has a mean diameter of bar x = 74 millimeters. (4 points) Construct a 96% two-sided confidence interval on the mean piston ring diameter. (4 points) What is the confidence level associated with the following confidence interval: 73.795

Solution

1a)

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

1

Sample Mean

74

Sample Size

25

Confidence Level

96%

Intermediate Calculations

Standard Error of the Mean

0.2000

Z Value

2.0537

Interval Half Width

0.4107

Confidence Interval

Interval Lower Limit

73.59

Interval Upper Limit

74.41

1b)

CI=(73.795,74.205)

Mean =74

Interval Half Width =0.205

Z value =0.205/0.2 =1.025

The corresponding p value =0.30

The required confidence level =   1-0.30= 0.7= 70%

1c)

In the 96% confidence interval is wider than that of 70% confidence interval

2a)

Sample mean =40

Half width =1

half width =1=z*se

1=z*2.5

Z=0.4

The confidence level =0.6892

The type I error =0.6892

2b)

Z value corresponding to 3% =2.17

1=z*12.5/sqrt(n)

Sample size = 2.17²*12.5² =735.76

The required sample size =736

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	1
Sample Mean	74
Sample Size	25
Confidence Level	96%
Intermediate Calculations
Standard Error of the Mean	0.2000
Z Value	2.0537
Interval Half Width	0.4107
Confidence Interval
Interval Lower Limit	73.59
Interval Upper Limit	74.41