Question

In an experiment involving the breaking strength of a certain type of thread used in personal flotation devices, one batch of thread was subjected to a heat treatment for 60 seconds and another batch was treated for 120 seconds. The breaking strengths (in N) of ten threads in each batch were measured. The results were

60 seconds:     43    52    52    58    49    52    41    52    56    58
120 seconds:   59    55    59    66    62    55    57    66    66    51

Let μXμX represent the population mean for threads treated for 120 seconds and let μYμY represent the population mean for threads treated for 60 seconds. Find a 99% confidence interval for the difference μX−μYμX−μY . Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.

The 99% confidence interval is

Answer 1

Answer:

Let X be the strength of thread treated for 60 seconds and Y be the strength of thread treated for 120 seconds.

similarly mean of Y = 59.6

and standard deviation Y = 5.296

Since the population standard deviations are not known two sample independent t-test should be used.

We need to construct the 99% confidence interval for the difference between the population means μ1​−μ2​, for the case that the population standard deviations are not known. The following information has been provided about each of the samples