Quantitative Customer Methods for Business Assignment

Assignment Task

Questions

1. A hospitality association conducted a restaurant user satisfaction study across London and the results indicate that 20% of restaurant users are satisfied with their experience in restaurants across London. Of these users, 75% would recommend the restaurant to a friend.

In a random sample of 80 restaurant users, find the probability that less than 10 were satisfied and would recommend the restaurant to a friend.

2. A high street retailer offers a loyalty card to its customers. Customers receive a discount when using the card and the retailer benefits from additional sales. The regular shopper that does not participate in the loyalty card program spends £90 per month. In a random sample of 120 shoppers that participated in the loyalty card program, each shopper spent on average £100 per month with a standard deviation of £20 per month.

At a 5% significance level, is there reasonable evidence that shoppers participating in the loyalty card program spend more than those who do not participate on average?

3. The return of an investment is normally distributed with mean and standard deviation What is the probability that this investment will return:

• At least 3%?
• Between 4.1% and 4.8%?

4. A survey with 625 calculated that the average consumer credit borrowing in the UK is £4,000 per adult with a standard deviation of £2,500.

• Calculate the standard error of the sample average
• Estimate the mean consumer credit borrowing per adult using a 95% confidence interval.

5. Below is a contingency table comparing the salary level of recent graduates with the degree obtained:

• What is the value of the chi-square statistic for this table?
• What is the conclusion of a hypothesis test for independence with a critical value of 3.84?

6. An insurance company did a survey with 80 customers and found that 40% of its customers have both home insurance and motor insurance. The probability that a randomly selected customer has motor insurance is 0.7. What is the probability that a randomly selected customer has a home insurance given that it has a motor insurance?

7. A regression analysis was applied between sales in £ () and advertising in £ () across all the branchesof a major fashion outlet. The following regression function was obtained.

If the advertising budgets of a branch of the fashion outlet is £20,000, then what will be the predicted sales level?

8. A company believes that its customers are willing to pay £40 for its product. In order to verify this assumption, they carry out a survey with 256 customers. The sample average of the survey was £38 and the sample standard deviation was 32. If the company wants to test the hypothesis that the mean willingness to pay is less than £40 what would be the value of the z statistic?

9. A financial institution offers a semi-annual bonus to salespeople in a particular department. Under this scheme, a bonus of 5% of the salesperson’s total half-year sales margin is payable if their mean monthly sales margin over the period exceeds £85k.

A salesperson has achieved monthly sales margin over the 1st half of this year as follows:
 

• Assume that individual monthly sales margins are normally distributed, do we have evidence to determine whether examine whether the mean monthly sales margin exceeds £85k at a 95% confidence level?
• An asset management firm advertises its AI algorithmic trading fund can provide a return of 2% for its clients. In a sample of returns from 9 clients the sample average was 1.6% with a sample standard deviation of 0.4%. Find a 99% confidence interval for the mean.
• The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 4,200 miles. The manufacturer guarantees the tread life of the tires for the first 54,960 miles. What is the proportion of the tires that will need to be replaced under warranty?

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