Read Confidence Intervals and P-values in Section C of your Lecture Workbook or on Cecil under Assignment Resources. Consider a study to determine ways the response rate in surveys can be improved. Two types of approaches are under consideration - telephoning prior to mailing out or not telephoning prior to mailing out the survey questionnaire. Telephoning people would create additional expenses. Therefore the question is, does telephoning people prior to mailing out the survey questionnaire have a beneficial effect on the response rate? In addition, market research companies consider that a difference in response rate of less than 8% would be of no consequence, whereas a difference of 8% or more could result in considerable benefits. Some possible outcomes of the study are:
Notes: 1. P_{Tel} - P_{NoTel} = the difference between the true proportion of people who would respond to the survey having received a telephone call (P_{Tel} ) and the true proportion of people who would respond to the survey having not received a telephone call (P_{NoTe}).
2. The hypotheses associated with the quoted P-values are:
H0 : P_{Tel} - P_{NoTel} = 0 vs H1 : P_{Tel} - P_{NoTel} ≠ 0
(a) (i) What is the hypothesised value?
(b) Which case(s) demonstrates, at the 5% level, that the difference in the sample proportions between the response rates for the two survey approaches, , is statistically significant?
(c) For which case(s) are we able to claim that the underlying difference between the response rates for the two survey approaches:
(i) is clearly big enough to have practical significance?
(ii) is too small to have practical significance?