ECON 227 A.J. Jones has collected data on white-collar employees under 30 years

Question

ECON 227 A.J. Jones has collected data on white-collar employees under 30 years of age in the 3 rival cities of Eurelia, Begonia, and Gorgon. Each of the employees sampled agreed to complete a standardized test. In a very short preliminary study Jones took sample scores from each of the cities. After the preliminary s Jones calculated mean scores and sample standard deviations samples tudy for 6 With Job Security City Eurelia 512 Begonia 602 Gorgon 711 Mean Std Dev Sample Size 72 75 82 112 155 Without Job Security Sample Size City Eurelia 550 Begonia 698 Gorgon 795 Mean Std Dev 24 53 58 21 288 345 Form a 95% confidence interval for the mean test score of white-collar Eurelians without job security. 1. a) How large a sample would have to be taken in order to form a 92% confidence interval for the mean test score of white-collar b) Begonians with job security? Test at the 5% level whether the mean test score of white-collar Eurelians with job security is significantly different from the mean test score of white-collar Eurelians without job security.

Explanation / Answer

a)
t value at 95% CI = 2.0860
CI = mean +/-t *(s/sqrt(n))
= 550 +/- 2.0860 *(24/sqrt(21))
= (539.0751, 560.9249)

b)
There was an error in this question since, the margin of error is not give.

c)
Hypothesis:

null hypothesis: mu1 = mu2
Alternative hypothesis : mu1 not equal to mu2

Test statistic:

x1 = 512 , x2 = 550 , s1 = 72, s2= 24 , n1 = 7 , n2 = 21

t = (x1 - x2)/ sqrt(s1^2/n1 + s2^2/n2)
= ( 512 - 550)/ sqrt ( 72^2/7 + 24^2/21)
= -1.3712
p value is calculated using t = -1.3712 with df = 26 at 0.05 significance level
P value = 0.1821

We fail to reject the null hypothesis. because p value is greater than significance level

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