Question

A survey is conducted to estimate the average household income in a large metropolitan area.

A random sample of 150 households in this area yielded an average household income of $55,000 with a standard deviation of $13,200.

(a) Construct a 95% confidence interval for the mean household income in this area. (Choose the BEST answer)

(b) All other information remaining unchanged, which of the following would produce a wider interval than the 95% confidence interval constructed above from Problem (a)?

(I) A sample with a standard deviation of $11,670 instead of $13,200

(II) An 80% confidence interval rather than a 95% confidence interval

(III) A sample size of 160 instead of 150

(IV) A sample with a standard deviation of $15,000 instead of $13,200

(V) A sample size of 175 instead of 150

A sample size of 175 instead of 150

Answer 1

55000   1.976 ( 13200 / 150

55000   2129.7

( 52870 , 57130 )

A 95 % CI for population mean is ( 52870 , 57130 )

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b)

A sample with standard deviation of $ 15000 instead of $ 13200, produce wider interval

option IV is correct.

As the standard deviation increases width of the interval also increases.