Ilu) ill TOWI B, I1 men were randomly chosen and their 6. (Exercise 13 t% ihts (

Question

Ilu) ill TOWI B, I1 men were randomly chosen and their 6. (Exercise 13 t% ihts (nches) measured. 15 cofhtmue heig 68.0 66.0 66.6 69.8 68.0 70.0 70.3 65.7 75.9 with an exploratory plot of this set and describe the distribution. a 95% t confidence interval for the difference in mean height between from town A and B. State your interpretation. (c) There is an outlier in town A. Remove this measurement and re-create the 95% t confidence interval. Does your conclusion change? 17. Run a simulation to see if the t ratio T- = (X-)/(S/Vn) has a t distri or even an approximate t distribution when the samples are drawn from a non- normal distribution. Be sure to superpose the appropriate t density curve onto your histograms. Try two different nonnormal distributions and remember to see if sample size makes a difference. 18. In the remark on page 181, we stated a result for the confidence interval for the difference in means if we knew that the population variances are the same. We also cautioned against using this result since, in general, it is difficult to

Explanation / Answer

Proportion of time 0 in confidence interval pooled and confidence interval unpooled is same i.e.0.9493

So we can conclude that population variances are same.

And also if we repeat the simulation with different sample sizes we conclude that population variances are same.

1)m=80,n=40

Proportion of time 0 in pooled as well as unpooled confidence interval=0.9507

2)m=120,n=80

Proportion of time 0=0.9515 for both confidence interval

3)m=80,n=80

Proportion of time 0 =0.9523 for both confidence interval

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