Question

a)Describe how a Confidence Interval might be better piece of information to report from a study than a hypothesis test

b)If we want to use the Margin of Error to set a meaningful real world threshold to consider an effect significant, give an example how you can use Margin of Error to determine the sample size

c)Explain why it is not correct to state that there is a 95% chance that the population mean lies within the interval.

Answer 1

(a) A common person easily understands the confidence interval. The hypothesis test is not easy to understand for a common man. Confidence intervals provide information about a range in which the true value lies with a certain degree of probability. A confidence interval provides a range of values that are likely to contain the population parameter of interest. A confidence interval calculates the probability that a population parameter will fall between two set values.

(b) The margin of error tells us how many percentages points our results will differ from the real population value. For example, the margin of error for the population mean is given by

The margin of error =   =  

where n is the sample size.is population sd, =level of significance

Given Margin of error =2.5,=0,05 population sd= 10 , find sample size n

we have

2.5 = 1.96*10/

= 19.6 / 2.5

n=61.46 =61

n=61

(c) A confidence interval, in statistics, refers to the probability that a population parameter will fall between two set values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. The 95% confidence interval does not imply a 95% chance of containing the population parameter is because the confidence interval is an answer to a different question. Confidence interval contains all values for which the data do not reject the null hypothesis that the parameter is equal to that value. That tells us nothing about the probability that the parameter is in the interval.