Question

# The laboratory experts its experiment this time testing 18 test tubes and finding it took reheating...

The laboratory experts its experiment this time testing 18 test tubes and finding it took reheating them an average of 1375 times until they cracked, with a standard deviation of 291. Compute the 95% confidence interval to estimate the mean number of times they can use the test tube. Does this support the test tube company's claim that the tubes can be used more than 1400 times before they crack?

Given that

mean = 1375

standard deviation = 291

sample size n = 18

degree of freedom = n-1= 18-1 = 17

t critical = 2.11 (using t distribution table with alpha = 0.05 and df =17)

Confidence interval =

it is clear that 1400 is included in the confidence interval and the upper limit of confidence interval is greater than 1400, so it is significantly more than 1400

therefore, it is supporting the test tube company's claim that the tubes can be used more than 1400 times before they crack