1. Starting salaries of 50 college graduates who have taken astatistics course h

Question

1. Starting salaries of 50 college graduates who have taken astatistics course has a mean of $42,786 and a standard deviation of$8,912. a.) Find the critical value zc corresponding to aconfidence level of c = 0.97 and construct a 97% confidenceinterval for the mean starting salary. Interpret the 97% confidenceinterval. b.) Suppose that the population standard deviation is actually9000. Find the minimum sample size needed to estimate thepopulation mean starting salary with 99% confidence. 1. Starting salaries of 50 college graduates who have taken astatistics course has a mean of $42,786 and a standard deviation of$8,912. a.) Find the critical value zc corresponding to aconfidence level of c = 0.97 and construct a 97% confidenceinterval for the mean starting salary. Interpret the 97% confidenceinterval. b.) Suppose that the population standard deviation is actually9000. Find the minimum sample size needed to estimate thepopulation mean starting salary with 99% confidence.

Explanation / Answer

n= 50
mean , = $42,786
standard deviation , = $8,912.
standard error, e = /n =1260.35
a.) for 97% confidence, z = 1.89
interval for the mean starting salary= ± ze = 42786± 1.89 x 1260.35 = (40403.94, 45168.06) b.) Suppose that the population standard deviation is actually9000.
the minimum sample size needed to estimate the population meanstarting salary with 99% confidence=??
for 99% confidence, z = 2.58
=9000
40403.94 = - ze
so, 40403.94 = 42786 - 2.58 x e
hence, e = 932.28
hence, /n = 932.28
so, 9000 / n = 932.28
hence n ˜ 95
minimum sample size needed =95

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