A research firm conducted a survey of 49 randomly selected Australian to determine the mean amount spent on coffee during a week. The sample mean was $20 per week. The population distribution is normal with a standard deviation of $5.

1. What is the point estimate of the population mean? Explain what it indicates.
2. Using the 95% level of confidence, determine the confidence interval for . Explain what it indicates. Instead of 49, suppose that 64 Australian were surveyed about their weekly expenditures on coffee. Assume the sample mean remained the same.
3. What is the 95% confidence interval estimate of ?
4. Explain why this confidence interval is narrower than the one determined in the previous exercise.