Question

A certain adjustment to a machine will change the length of the parts it makes but will not affect the standard deviation. The length of the parts is normally distributed, and the standard deviation is 0.5 mm. After an adjustment is made, a random sample is taken to determine the mean length of parts now being produced. The resulting lengths are as follows.

74.8

75.5

74.4

76.1

74.3

75.3

76.5

74.1

76.0

74.8

(a) What is the parameter of interest?

> standard deviation length

> sample size    

> change in mean since adjustment

> mean length

(b) Find the point estimate for the mean length of all parts now being produced. (Give your answer correct to two decimal places.)
__________ mm

(c) Find the 0.99 confidence interval for μ. (Give your answer correct to three decimal places.)
( _____ ,_____ )

Answer 1

(a) Parameter of interest

mean length

(b) point estimate for the mean length of all parts now being produced : Sample mean :

Given,

Sample size : n= 10

x : Length of parts :

	x: Length of part
	74.8
	75.5
	74.4
	76.1
	74.3
	75.3
	76.5
	74.1
	76
	74.8
Total	751.8

Sample mean :

point estimate for the mean length of all parts now being produced : Sample mean : = 75.18

(c)

Given,

Population standard deviation : = 0.5

Formula for Confidence Interval for population Mean : When Population Standard deviation is known

for 99% confidence level = (100-99)/100 = 0.01

/2 = 0.01/2 = 0.005

Z_/2 = Z_0.005 = 2.5758

0.99 confidence interval for

0.99 confidence interval for = (74.773 , 75.587)