Previous market research at a high street coffee shop has found that 20 percent of customers buy cake with their morning coffee. You have been tasked with calculating the sample for a new survey to understand the cake consumption of morning coffee customers.

(a) What formula should be used for this calculation? Explain the formula.

(b) If the acceptable error is 5 percent and we wish to be 95 percent confident, what sample size should be collected?

(c) If the acceptable error is just 1 percent, what sample size is required?

(d) If the confidence level is relaxed to 90 percent, what are the new sample sizes for (b) and (c)?

(e) Should the data be collected using a probability or nonprobability sample? What are the advantages and disadvantages of each method?