Mr. Thomas joined First Buy, an FMCG company, in April 2017. Thomas reported to Ms. Bishop.

At the end of October 2017, the senior management team of First Buy got the information from

the regional heads that, on average, the sales had gone up by 20% in Eastern and Southern regions,

whereas the North and West regions had shown a flat sales growth of 10% in the second quarter

(July-Sep'17). Although the team had not seen the actual sales figures or any such analysis, the

estimates suggested that it was not different from the trend observed in past four quarters, unless

verified. In fact, one of the regional heads quoted that the variation in the sales growth as captured

by standard deviation, over the past few years in all four regions is about 4%. The management

knew that this growth was not driven by the marketing and advertising expenses as the budget is

almost equally allocated to each region. They thought that improvement in sales growth in the East

and South regions might be driven by the change in employee composition. There had been some

new recruitment having background of MBA in marketing & sales in these two regions in the past

one year. In fact, the perception was that 60% of the sales executives have MBA background.

Mr. Bush was a member of the senior management team. Ms. Bishop reported to Mr. Bush.

Mr. Bush asked Ms. Bishop to analyze historical sales data and find the likelihood of gap or the

probability of error between the perceptions (or expectation) of the senior management team and

the actual data. The analysis and the presentation had to be prepared in just 2 days. Thomas was

pulled up in the project. The first review of the project was expected in one day. Ms. Bishop had

advised Thomas to work with four and half years (Apr'13-Sep'17) of sales data (approx.) for all

the four regions (North, East, South and West). Thomas knew the data source, but he also knew

that collecting four and half years of data would take more than half a day. This made Mr. Thomas

wondered how he should proceed to extract the data and analyze the results without missing the

deadline.

By the end of the day, Thomas derived that the average sales growth for the data span is 15% for

54 observations (i.e. four and half years of monthly sales figures) and the percentage of sales

executives having MBA background is around 45% in the Eastern and Southern regions. He also

noted that out of total 2000 sales employees, only 400 were employed in the East and South zones.

a) Find the probability that Mr. Thomas's estimates of average sales growth and percentage

of employee having MBA fall within 5% of management's perception in both cases?

b) If the level of confidence is maintained at 99%, please check whether the sample size used

for the study is adequate to attain a margin of error of 25% in case of mean sales growth

estimation.

c) Can you derive a 95% confidence interval for mean sales growth for Eastern and Southern

region?