1. Two hundred people were sampled about their holiday gift spending, finding the average expenditure for gifts is $1200. Assume the population standard deviation is $350.

1a) Calculate the 99% confidence interval for the population mean.

1b) Calculate the 95% confidence interval for the population mean.

1c) Calculate the 99% confidence interval for a sample of 500 people.

1d) What would happen to the 95% confidence interval if you increased the sample size?

1e) If you were to conduct a study on your own, which confidence level would you choose?

2. The mean salary of teachers in Nebraska is $45,000 per year. A sample of 100 teacher salaries in unionized school districts in Nebraska show a mean of $49,000 per year, with a standard deviation of $4000.

2a) Calculate the confidence interval for unionized teacher salaries in Nebraska. Use a 95% confidence level.

2b) Based on the confidence interval you just calculated, does the state-wide salary for all teachers differ from unionized ones?

3. A popular coffee chain wants to estimate how long customers wait in their drive through to order their drink. They would like to get an estimate within 1 minute. For the calculation, management uses a planning value of 3.5 minutes for the population standard deviation.

3a) How many customers do they need to sample to get the mean waiting time within their desired 1-minute margin of error? They want to be 95% confident in their result.

3b) How many people would they need to sample to be 99% confident?

4a) A grocery chain wants to estimate the proportion of customers that are subscribed to their store card (loyalty program) within 3%. Competing chains find it is 68%, and they are going to use this for their planning proportion for their study. How many people do they need to sample to reach their target accuracy at 95%?

4b) What if they instead shrink their acceptable margin of error down to 2%?

4c) What if they don't have a planning proportion (2% ME)?