Question

Construct a 95% confidence interval for the population mean,Assume the population has a normal distribution, A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a standard devastion of 31 hours.

From the above question calculate the 99% confidence interval for n = 16.

then, Letting n= 100, calculate the 95% and 99% confidence intervals

(a) What happend to the interval width from 95% to 99%

(b) what happend to the interval width from n =16 to n =100?

Answer #1

For n = 16

At 95% confidence interval the critical value is t^{*} =
2.131

The 95% confidence interval for population mean is

+/- t^{*} * s/

= 645 +/- 2.131 * 31/

= 645 +/- 16.515

= 628.485, 661.515

At 99% confidence interval the critical value is t^{*} =
2.947

The 99% confidence interval for population mean is

+/- t^{*} * s/

= 645 +/- 2.947 * 31/

= 645 +/- 22.839

= 622.161, 667.839

For n = 100

At 95% confidence interval the critical value is t^{*} =
1.984

The 95% confidence interval for population mean is

+/- t^{*} * s/

= 645 +/- 1.984 * 31/

= 645 +/- 6.15

= 638.85, 651.15

At 99% confidence interval the critical value is t^{*} =
2.626

The 99% confidence interval for population mean is

+/- t^{*} * s/

= 645 +/- 2.626 * 31/

= 645 +/- 8.141

= 636.859, 653.141

a) The interval width increases from 95% to 99%.

b) The interval width decreases from n = 16 to n = 100.

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mean μ using the t-distribution.
c = 0.95, = 645, s = 31, n = 16

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