Question

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

Answer 1

The sample data should be collected in such a manner that it is:

1. Consistency

As a researcher one should be confident that changes in population data is reflected in sample data.

2. Diversity

This is a really important characteristic of a sample as population is sensitive to local diversities. It can be avoided by taking a diverse sample

3. Transparency

The researcher must discuss about how the sample lacks in totally representing the population. This will be further used in discussions regarding the conclusions formed on the basis of sample data.

In this particular situation, we have to select a sample of clients from the entire client list of a large financial firm with the goal of analysing how many have a particular threshold.

It is clearly observable that no strata can be formed. This is because diving the population on terms of gender, age or any other aspect might lead to biased sample. As we have no division of a pre-determined amount of investmenr=t by each client, strata on the basis of this cannot be formed.

In such a scenario following sampling techniques can be used

1. Simple Random Sample

In this method we will take the entire population of client list of this financial firm and form a sample. In this type of sampling, each and every member has an equal chance of being a part of the sample. This method is best suited for a smaller population where the entire population can be named or numbered. This condition is satisfied in out case making this a suitable method of usage.

The simple random sample formed is unbiased and is suited for drawing conclusions. This will result in a sample which is representative of the population and hence we will be able to derive accurate results

This can be done using various techniques which will affect the data collection in the following manner

a. Picking random clients from the list

b. Using random numbers to form the sample

In either of the method, we will have to prepare a curated list of the clients and then pick up a random sample. Data Collection in this method will be based on already present documents and records with the company.

The limitation of this method include :

a. The task of forming the entire list of clients. This is a huge task as it will consume a lot of time, effort and money

b. Sampling errors like human errors have a high chance of seeping through.

Another technique that we can use is

2. Convenience Sampling

In this sampling technique, sample is picked up on the basis of convenience, accessibility, reach and availability. In this method a sample can be collected very quickly and our required preliminary research can be conducted.

In this method, the methods of data collection that can be used are:

a. Interview various employees about their clients

b. Make a proper questionnaire for employees about the clients they handle

This will also require the employees to look into their documents and records.

c. They can also be collected on the basis of the number of clients who contacted the large financial firm on a particular day or came into their office.

The major problem with using this method is that the sample is not reliable. However a preliminary research can be carried out.