Due to the war between Russia and Ukraine, petrol prices have increased significantly. To ease the pressure from increasing fuel costs, the Australian government plans to provide financial assistance. In order to arrange the funds, they approached you to help them find out how much Australians spent on fuel every week. Based on a recent survey involving 50 Australians, you know that the average weekly spend on fuel is $120. The government also informed you that the standard deviation of weekly fuel expenses of all Australians is $35. Based on the given information, respond to the following question

Develop a 99% confidence interval estimate of the population mean.

Develop a 95% confidence interval estimate of the population mean

Develop a 90% confidence interval estimate of the population mean

What changes can you notice from the width of the confidence interval as the confidence level decreases? Explain why this is the case

What changes do you expect in the confidence interval widths if the sample size was larger than 80? Explain why.