Question

Question 5 (3 points) Saved A sample of 15 test-tubes tested for the number of times they can be heated on a Bunsen burner before they cracked found that the average of the 15 tested was 1230 and the sample standard deviation was 270 times. Construct a 99% confidence interval for the average number of times all test tubes can be heated on a Bunsen burner. We are 99% confident that the average number of times that test tubes can be heated on a Bunsen burner is between A/ and A times.

Answer 1

Solution :

Given that,

$\bar x$ = 1230

s = 270

n = 15

Degrees of freedom = df = n - 1 = 15 - 1 = `4

At 99% confidence level the t is ,

$\alpha$ = 1 - 99% = 1 - 0.99 = 0.01

$\alpha$ / 2 = 0.01 / 2 = 0.005

t_{$\alpha$ /2,df} = t_0.005,14 =2.977

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 2.977 * ( 270 / $\sqrt$ 15)

= 207.53

Margin of error = 207.53

The 99% confidence interval estimate of the population mean is,

$\bar x$ - E <$\mu$  < $\bar x$ + E

1230 - 207.53 < $\mu$ < 1230 + 207.53

1022.47 < $\mu$ < 1437.52

(1022.47,1437.52 )