Show transcribed image text HA82 ←ラC 을Secure https://www.webassign.net/web/Student/Assignment.R a ☆ standard normal distribution This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider random sample of size n = 31, with sample mean x-45.7 and sample standard deviation s-5.3. (a) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 95% ower limit 43.78 upper limit 48 62 42 14 X 49.26 X40.78 x 50.02 筭 (b) Compute 90%, 95%, and 99% confidence interval Use s as an estimate for σ. Round endpoints to two digits after the decima Is for μ using Method 2 with the standard normal distribution, 90% 99% lower limit 42.95 upper limit 4844 4140 8.97 (e) Compare intervals for the two methoda. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal Yes, The respective intervals based on the t distribution are longer O No. The respective intervals based on the t distribution are longer. Yes. The respective intervals based on the t distr bution are shorter. No. The respective intervals based on the t distr bution are shorter (d) now consider a sample i20 of S. Cernpute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to tvro digits after the decimal – 90% 95% 994s lower Imit upper imt (e) Compute 904. 95%·and 99% confidence intervals for " using Method 2 with the standard normal d.mbution Uae s as an estimate for a. Round endpgints to tvio digits after the decimal. 95 lower Imit upper lim 09