2. Commuting in Calgary. Each person in two independent large random samples of

Question

2. Commuting in Calgary. Each person in two independent large random samples of male and female working adults in Calgary. Canada, was asked how long, in minutes, his or her typical daily commute was The 99% confidence interval for the difference between true mean commute times for male and female working Calgary residents, ( , 2 ), is (-3.97 minutes, 6.37 minutes ) a. This interval presents no convincing evidence at -001 that mean commute times for male and female working Calgary residents are different. Explain why b. Give an example ofconfidence interval for( 1-2 ) that would : (i) Strongly suggest that 1 2 (ii) Strongly suggest that 1SH2

Explanation / Answer

By 95% confidence interval we mean to say that,we are 95% confident that the parameter value will lie within the interval.,under alpha=0.01,the confidence coefficient is=1-alpha=99%,so 99% confidence interval is (-3.97,6.37) .Now see that,this is a vast interval which contains the value 0 and its neighbourhood,so 99% of times the value of the true difference paramter lies anywhere within the interval,it may be 0,it may be 4.So,we have no evidence such that we can say that the true population difference differs from zero because our 99% confidence interval contains 0,so it may happen that most of the times 0 comes,or most of the times 4 comes,we can not say about any particular value clearly.So,we have no clear evidence that the difference differs from 0.

b.

i)So,if 99% confidence interval is suppose (3.89,7.3),so we are 99% confident that the difference is positive ,ie mu1>mu2.See that,this interval does not contain any neighbour hood of theta

ii) Suppose 99% confidence interval is (-7.3,-3.89),so we are 99% confident that the difference is negative,somu1<mu2.So we have enough evidence to conclude this.This is the way,confidence interval works.

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