Question

1) When forming confidence intervals and doing hypothesis tests for a single mean, we were able to use the standard normal distribution when the sample size exceeds 30. What two things happen at the large sample size which allow us to use the standard normal?

2) Why would you want to put a claim that you want to support into the alternative hypothesis rather than the null hypothesis?

3) Why must an equality hypothesis (i.e., that a population parameter equals one specific value) be in the null hypothesis?

4)Explain, in terms of variation, why a paired difference approach might be preferable to an independent group means approach in assessing whether the means of two different groups are different?

Answer 1

1).a) sample size equals to 30 is the minimal sample sizes is to provide adequate power to distinguish normal distribution from other distribution so that failure to find significant deviations from normality carries with it a reasonable degree of confidence interval that the data are consistent with that distribution .the no of observations needed depends on the alternative distribution of interest.

b) the number 30 also comes from examining the chi square diatrdistrib.the number greater than 30 are enough to show it to follow Normal distribution.

2) We always put a claim to support alternative hypothesis as the conclusion is always drawn about null hypothesis.so , after drawing conclusion we are able to understand easily that when null hypothesis is reject then our claim to support alternative hypothesis is true otherwise it is wrong.

3) The reason behind it is also same as in 3rd question and in addition to that here we know that as the sample is getting larger and larger then the fixed value converges to the population parameter.

4) paired difference in approach might be preferable to an independent group means approach in assessing whether the means of two different groups are different because In pair test of means we are able to measure the amount of variation occurred before applying treatment than after applying treatment.here we able to measure the exact effect of treatment on the selected groups but In testing of means of two different groups we are not able to clearing the amount of variation occurred between the two groups.