Question

​a) If the confidence interval for the difference in population proportions p1​ - p2 includes​ 0, what does this​ imply? ​

b) If all the values of a confidence interval for two population proportions​ are​ positive, then what does​ this​ imply? ​

c) If all the values of a confidence interval for two population proportions​ are​ negative, then what does​ this​ imply?

d) Explain the difference between sampling with replacement and sampling without replacement. Suppose you had the names of 10​ students, each written on a 3 by 5​ notecard, and want to select two names. Describe both procedures.

Answer 1

Part a

If the confidence interval for the difference in population proportions p1​ - p2 includes​ 0, this is implies that there is no statistically significant difference in the two population proportions.

b) If all the values of a confidence interval for two population proportions​ are​ positive, then this is implies that there is a statistically significant positive difference exists between the two population proportions.

c) If all the values of a confidence interval for two population proportions​ are​ negative, then this is implies that there is a statistically significant negative difference exists between the two population proportions.

d) In the procedure of sampling without replacement, we select the first item or observations at random and then we do not replace this selected item in the targeted population or sample space. In the procedure of sampling with replacement, we select the first item or observation at random and then we replace this item or observation into original source of population from where we select the observations randomly. In the sampling with replacement, the probability of selection of item at each time remains same because we replace the selected item or observation into population. In the sampling without replacement, the probability of selection of item at each time does not remain same because we do not replace the selected item into population.

Suppose, we are given names of 10 students, then by using sampling with replacement we will select first student name randomly and then we replace this name card in the set of 10 name cards. In this selection process, the same name can be selected twice or more times. By using sampling without replacement, we will select first name card at random and then we will not replace this name card again the remaining set of name cards. So, probability of selection of each name card will change at each time.