1. Math
  2. Statistics And Probability
  3. of the clients of a a marketing consultant was commissioned...

Question: of the clients of a a marketing consultant was commissioned...

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of the clients of a A marketing consultant was commissioned to conduct a questionnaire survey large financial services company. The total number of respondents was 650, of whom 220 had investments above a specified threshold Each respondent who had investments above the threshold was asked about the percentage of these investments that was held in the form of a certain type of trust. The respondents answered by ticking appropriate boxes and the results led to the following frequency percentage 0-10 10-25 25-50 S0-100 frequency22 76 73 49 ) Write explanatory notes on ANY TWO sampling methods for the above survey and clearly highlight how they could find application in collecting data for the above data.[8 marks] (i) Use the midpoint of each interval to calculate the mean percentage for the full set of 220 such respondents, assuming that the frequencies in each category are uniformly spread over the corresponding range 3 marks) The same respondents with investments referred to above were also asked to specify their satisfaction with the current return received from their full portfolio of investment. This was in the form of a four-point qualitative scale: very satisfied, quite satisfied, a little disappointed, very disappointed. The following two-way table of frequencies was obtained. percentage in type of trust <10 10-25 25-50 >50 very satisfied quite satisfied a ittle disappointed 0 37 28 15 very disappointed 3 421 29 36 27 In order to investigate whether there is any relationship between the percentage in such trusts and satisfaction with current return, a chi-square test is to be by combining the very satisfied and quite satisfied categories together and the a little disappointed and very disappointed categories together result in the following reduced two-way table. percentage in type of trust 10 10- 25 25-50 >50 9 35 43 33 3 41 30 16 sotisfied (ni) Calculate the expected frequencies for the above table under an appropriate hypothesis (which should be stated) and perform the required χ2 test at the 5% level using this reduced table and comment on your conclusion. 8 marks) and o(3)- 7.815 (v) Calculate a 95% confidence interval for the percentage of such investors who would have investments above the threshold [6 marks

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