Hello, Attached you will find a screenshot of the problem. Thank you for your help! Sample Size AnalysisConsider the same simple random sample. This time we'll keep the level of confidence constant and vary the sample size. Round results to 1 decimal place.\[\bar{x} = 63 \, mph\]\[s = 10 \, mph\]1. Construct the 95% confidence interval for vehicle speeds with n = 50.2. Construct the 95% confidence interval for vehicle speeds with n = 100.3. Construct the 95% confidence interval for vehicle speeds with n = 500.In 1-2 complete sentences, describe the effect of increasing the sample size on the confidence interval.Submissions- Take an image of your completed work, or scan and save your work as a PDF document.

Given, mean (x̅) = 63 sample standard deviation (s)= 10 a) sample size (n) = 50 degree of freedom = df = n -1 = 50-1 = 49 significance level α = 0.05 tcritical = tα/2 ,df = 2.0086 95 % confidence interval for true mean is given by = x̅ ± tcritical *s/√n = 63 ± 2.0086*10/√50 = 63 ± 2.8406 = (60.1594,65.8406) b) sample size (n) = 100 degree of freedom = df = n -1 = 100-1 = 99 significance level α = 0.05 tcritical = tα/2 ,df = 1.984 95 % confidence interval for true mean is given by = x̅ ± tcritical *s/√n = 63 ± 1.984*10/√100 = 63 ± 1.984 = (61.016,64.984)c) sample size (n) = 500 degree of freedom = df = n -1 = 500-1 = 499 significance level α = 0.05 tcritical = tα/2 ,df = 1.9647 95 % confidence interval for true mean is given by = x̅ ± tcritical *s/√n = 63 ±1.9647*10/√500 = 63 ± 0.8786 = (62.1214,63.8786)Increasing the sample size decreases the margin of error and makes the confidence interval narrower.