Question

2:30 PM Thu Apr 16 $ 75% '< U 5 TODO 40 ° to Stat 350 Spring 2020 Exam 2 04/16/2020 Name: Roster Number: Show your work for full credits and keep 4 decimals when needed. 1. The basal diameter of a sea anemone is an indicator of its age, and it is assumed to be normally distributed. The diameters of 25 randomly picked anemones yielded a mean of 4.7 cm and a standard deviation 1.5 cm. (a) Construct a 90% confidence interval for the population mean. (10 points) (b) Based on the standard deviation of above random sample, researchers plan to design a new study to construct a new confidence interval with a standard error of 0.2 cm. How large a sample do the researchers need to take? (6 points)

Answer 1

The 90% confidence interval for the population mean is as follows: where, = Sample mean s = Sample standarddeviation n=Sample size ta = Critical value

It is given that n= 25. X = 4.7, and s=1.5. From the Table of t-distribution, we can find the critical value. The critical value oft at 0.10 significance level and 24 degrees of freedom istoos = 1.71. The 90% confidence interval for the population mean is as follows: CI = i + = 4.7+1.7153 = 4.7 +0.513 =(4.187,5.213) Thus, the 90% confidence interval for the population mean is (4.187.5.213).