Question

The chemistry department sampled 15 test tubes to see the number of times they can be heated on the Bunsen burner before they cracked. The sample mean was 1230 times with a standard deviation of 270. Estimate the average number of times a test tube can be heated before it cracks at a 90% confidence level. You do not need to check conditions. Be sure to interpret your answer in a sentence.

Answer 1

Given that,

= 1230

s =270

n = 15

Degrees of freedom = df = n - 1 = 15- 1 =14

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,14 =1.761    ( using student t table)

Margin of error = E = t_/2,df * (s /n)

=1.761 * (270 / 15) =122.7658

The 90% confidence interval estimate of the mean is,

- E < < + E

1230 - 122.7658 < <1230 + 122.7658

1107.2342 < < 1352.7658

( 1107.2342, 1352.7658)

average number of times a test tube be heated before it cracks for 90% confidence interval estimate (1107.2342, 1352.7658)