The manager of Apache Burger felt that an average of 70 customers made purchases daily between the hours of 3 p.m. and 5 p.m. A random sample over 50 days showed the sample mean to be 68.6 customers. Assume a population standard deviation of 8.2 customers.

Using the sample data, construct a 99% confidence interval for the population mean

a)Does the 99% confidence interval include the value suggested by the manager? Interpret this result.(1 mark)

b)Suppose you decided to switch from a 99 to a 95 percent confidence interval. Without performing any calculations, will the interval increase, decrease, or stay the same? Which of the values in the formula will change?

Question 2

You are to conduct a sample survey to determine the mean family income in a rural area. The question is how many families should be sampled? In a pilot sample of 10 families, the standard deviation of the sample was $500. The sponsor of the survey wants you to use the 95% confidence level. The estimate is to be within $100. How many families should be interviewed?