SOLUTION: According to a 2010 Business Week article, the average 401(k) account balance for individuals nearing retirement was $60,000. To test if this average has recently chan

Question 1061776: According to a 2010 Business Week article, the average 401(k) account balance for individuals nearing
retirement was $60,000. To test if this average has recently changed, suppose a sample of 30 people
starting retirement was selected and it found that the average 401(k) balance was $67,000. Assume the
population standard deviation was $21,000. Using an α = .05, answer the following:

a. State the null and alternative hypotheses.
b. What conclusions can be made about the current average balance of 401(k) accounts for
people nearing retirement?
c. Determine the p-value for this test and interpret its meaning.
d. Repeat the preceding hypothesis test using the critical value approach.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Ho: There has been no change mu o=mu
Ha: There has bee a change mu o ne mu
alpha=0.05 prob reject Ho|Ho is true
test statistic is z.
critical value is |z|>1.96
calculation z=(x bar-mean)/sigma/sqrt(30)
t=7000*sqrt(30)/21000=(1/3)*sqrt(30)=1.83
This is not greater than 1.96
Fail to reject Ho: insufficient evidence to say that there was a change.
p-value=0.068.
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