Task $1$: Statistical Consulting $[30$ Marks$]$

A local supermarket in Tingley introduced a loyalty card app in January $2023.$ Customers

buy groceries using the loyalty card app on their mobile phones. As a consultant to the

local supermarket, you have been asked to conduct a study to examine the frequency of

repeat purchases by customers. Specifically, you have been asked to assess whether

there is a disparity in repeat purchases between consumers who use the loyalty card

app and those who are not

The following research questions were set.

Is the proportion of consumers who use the loyalty card app greater than $50\%?$

Is the proportion of consumers who make repeat purchases different between those who

use the loyalty app and those who do not?

The following two sets of hypotheses were stated.

Null: $,$ The proportion of consumers who use the loyalty app is equal to $50\%.$

Alternative: The proportion of consumers who use the loyalty app is greater than $50\%.$

Null: $,$ The proportion of consumers who make repeat purchases is not different between

those who use the loyalty app and those who do not.

Alternative: The proportion of consumers who make repeat purchases is different

between those who those who use the loyalty app and those who do not.

A simple random survey was conducted among traditional supermarket shoppers.

Two of the questions, taken from the research instrument, are reproduced below.

Question $1$: Do you make repeat purchases?

No

Yes $$

Question $2$: Do you use the loyalty app?

No

YesAppendix $-$ SPSS Output for Part $2$

Required for Part $2($ comments for Part $2$ should not exceed $400$ words in total$)$

To complete the following, you need to refer to the output in the Appendix below.

The SPSS tables should be inserted into your report and used as statistical evidence.

Use either a snipping tool to copy the tables in the appendix or copy the tables $($saved

as PNG images$)$ from the file: $\text{'}$SPSS Evidence' in the coursework folder.

The tables are made available but a data set is NOT made available for Part $2.$

Tables can be found in the Appendix.

a$.$ Interpret Table $2\mathrm{.}1$ and prepare a short comment on your findings.

b$.$ Table $2\mathrm{.}2$ shows the output for a hypothesis test conducted to inform on research

question $1$ above. Interpret the output and prepare a short statistical report, in the

classical style, to summarise your findings. In your report, you need to state the

null and alternative hypotheses, name the hypothesis test conducted and fully

explain the output $($all relevant values$),$ calculate and interpret the effect size,

where relevant, and discuss the assumptions of the test.

Based on your statistical interpretation, write a second comment aimed at the

client to explain the outcome of the research in plain English.

c$.$ Table $2\mathrm{.}3$ shows the output for a hypothesis test conducted to inform on research

question $2$ above. Interpret the output and prepare a short statistical report, in the

classical style, to summarise your findings. In your report, you need to state the

null and alternative hypotheses, name the hypothesis test conducted and fully

explain the output $($all relevant values$),$ calculate and interpret the effect size,

where relevant, and discuss the assumptions.

Based on your statistical interpretation, write a second comment aimed at the

client to explain the outcome of the research in plain English.

NB: Up to $10\%$ of the marks is awarded for coursework management. Marks are

awarded for professional presentation, use of section and paragraph titles and starting

each task on a new page, among others.Appendix $-$ SPSS Output for Part $2$

Table $2\mathrm{.}1$

Table $2\mathrm{.}2$

Table $2\mathrm{.}3$