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 50 120

seconds: 59 55 59 66 62 55 57 66 66 51

Let μX represent the population mean for threads treated for 120 seconds and let μY represent the population mean for threads treated for 60 seconds. Find a 99% confidence interval for the difference μX−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

Given :

60 Seconds (Y)	43	52	52	58	49	52	41	52	56	50
120 Seconds (X)	59	55	59	66	62	55	57	66	66	51

Solution :

We have to calculate mean of X and Y,

Now we have to calculate the standard deviation of X and Y,

The degree of freedom can be calculated as,

The given confidence interval is 99% hence the significance level will be 1% i.e. , also

From the t distribution table, with degree of freedom = 17 and α/2 = 0.05, will be 2.898.

Therefore,

The confidence interval 99% is (2.638, 15.562)

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