Question 3. [ 10 marks ] [Chapter 7] Consider a study to determine ways in which

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Question 3. [ 10 marks ] [Chapter 7] Consider a study to determine ways in which 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 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 -wotelse(prd-PvoreP-value 0.0823 0.0139 0.0994 0.0989 0.0935 95% CI 0.054, 0.376) 0.025, 0.079) (-0.183, 0.207) (-0.161, 0.223) 0.159, 0.525) NoTe Case 1 Case2 Case3 Case4 Case 5 0.215 0.052 0.012 0.033 0.342 0.0090 0.0002 0.9039 0.7385 0.0003 Notes: 1. Pre PoTethe difference between the proportion of people who would respond to the survey having received a telephone call reand the proportion of people who would respond to the survey having not received a telephone call (PNoTel) The hypotheses associated with the quoted P-values are 2. (a) (i)What is the hypothesised value? (i) In which direction and how far away, in terms of standard errors, is the estimated difference [1 mark] in Case 1 (pTel-PmTel-0215 ) from the hypothesised value? [ 2 marks] (b) which case(s) demonstrates, at the 5% level, that the difference between the observed response rates for the two survey approaches, re-rore, is statistically different from the hypothesised value? For which case(s) are we able to claim that the true difference between the response rates for the two survey approaches: (i) has practical significance? (ii) does not have practical significance? In which case(s) have we learned nothing useful about the difference between the response rates for the two survey approaches? Suppose the actual outcome for the study is: [1 mark] (c) [1 mark ] [1 mark] (d) [1 mark ] (e) 95% Cl NoTe Case 6 0.168 0.0975 0.0848 (-0.023, 0.359) Write three to four sentences interpreting this output. You need to refer to statistical significance and practical significance. Which type of survey approach would you recommend? Give a reason(s) for your choice [3 marks]

Explanation / Answer

a). Observe the difference in response rate values. Only two values (0.052 and 0.342 ) have p value less than 0.005 (95 % confidence level) .This means that for these values our null hypothesis holds good.

But it is said that the companies will respect only the response rate difference of atleast 8 %.

Hence we reject value 0.052 (=5.2%) . The acceptable value is 0.342 or 34.2 % .

This is our hypothesised value.

a ii). The 95 % CI of case 1 is (0.054,0.376) . The hypothesised value lie to the right of the mean difference of 0.215 and is at a distance of (0.034) .

b). for statitically significent case the p value <=0.05 (5%)

clearly Only two values (0.052 and 0.342 ) have p value less than 0.005 (95 % confidence level) .This means that for these values our null hypothesis holds good. and other values (0.215 ,0.012, 0.033 ) are statistically different (ie alternate hypothesis is correct meaning that the difference in response rates is not zero.).

c).Answered in part b.

Statisitcally significent - case 2 ,case 5

Statistically insignificent case 1, case 3 ,case 4

d). case 3 as it is a sub set of case 5 and hence its reslut already implies from result of case 5.

e).The p vlaue is >0.05 (95% Confidence) .Hence the idfference of 0.168 (16.8 %) is not siginifcent to the assumption that the difference is response rates is zero.

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