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)

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