Data Analysis, please show all workThe amount of yearly rainfaill in Chicago was sampled. 40 years from the records was randomly checked. The mean rainfaill was 33.98 in ches, with a standard deviation of 5.22 inches.Provide 90%, 95%, and 99% confidence intervals for these values. Remember to provide your answer in the form of a properly phrased confidence interval statement.Suppose the sample size was doubled. How would this affect the confidence interval? You don't have to provide a quantitative answer here. Simply indicate if it would go up, down, or remain approximately the same.

Confidence interval is the range used to determine where the population mean lies. It varies based on the confidence interval. If the confidence level increases, the range become tighter or close. If the confidence interval decrease, the range become wider. a) Given : Amount of yearly rainfall in Chicago was sampled. Sample size is 40 Mean rainfall is 33.98 inches Standard deviation of rainfall is 5.22 inches Confidence interval at 90% : z critical value at 90% is 1.65 (From z table) Now, x¯±z0.10×σn=33.98±1.65×5.2240=33.98±1.36=33.98-1.36,33.98+1.36=32.62,35.34 The true population mean lie at the 90% confidence interval at the range 32.62 and 35.34 Confidence interval at 95% : z critical value at 95% is 1.96 (From z table) Now, x¯±z0.05×σn=33.98±1.96×5.2240=33.98±1.62=33.98-1.62,33.98+1.62=32.36,35.60 The true population mean lie at the 95% confidence interval at the range 32.36 and 35.60 Confidence interval at 99% : z critical value at 99% is 1.58 (From z table) Now, x¯±z0.01×σn=33.98±2.58×5.2240=33.98±2.13=33.98-2.13,33.98+2.13=31.85,36.11 The true population mean lie at the 99% confidence interval at the range 31.85 and 36.11b) Given : Let the sample size was double. If the sample size increases, the margin of error decreases. If the margin of error decreases, the closer the confidence interval range. Hence, the sample size increases the confidence interval range become small or go down.