The data below contain the number of defects observed on each of 50 lcd screens

Question

The data below contain the number of defects observed on each of 50 lcd screens made by a certain manufacturer.

Assignment 6q1 data

Construct a 95% confidence interval for the mean number of defects per screen for all screens produced by this manufacturer.

a) What is the lower limit on the interval? Give your answer to three decimal places. 1

b) What is the upper limit on the interval? Give your answer to three decimal places. 2
c) Based on the interval above, would you believe that the mean number of defects per screen for all screens from this manufacturer is 1.82?

Yes because 1.86 is not inside the interval. No because 1.86 is inside the interval.     No because 1.86 is not inside the interval. Yes because 1.86 is inside the interval.

d) If we are very certain that the true standard deviation of the number of defects per screen is below 2, what sample size would be required so that the width of the 95% confidence interval for the mean number of defects per screen is at most 0.27? Make sure you enter a whole number below. 4

defects 1 4 2 3 1 0 4 3 1 1 6 3 4 0 5 2 1 2 0 2 2 1 4 2 2 2 3 2 3 3 5 4 2 1 2 4 2 2 2 3 3 2 2 2 2 2 1 3 4 1

Explanation / Answer

M = 2.36
t = 1.96
sM = (1.32112/50) = 0.19

= M ± Z(sM)
= 2.36 ± 1.96*0.19
= 2.36 ± 0.3662

Result

M = 2.36, 95% CI [1.9938, 2.7262].

You can be 95% confident that the population mean () falls between 1.9938 and 2.7262.

a) Lower limit = 1.9938

b) Upper limit = 2.7262

c) No because 1.86 is not inside the interval.

d) 3

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