1.The records of a national mutual funds association indicate that the average mutual fund achieves annualized returns of 9.0%. Due to recent market fluctuations, the association believes the annualized returns are higher than 9.0%. In a study of 100 randomly selected funds, it was found that the average annualized return was 9.4% with a standard deviation of 2.2%. At the 5% significance level: a. The analyst can conclude that the annualized return has decreased. b. The analyst can conclude the annualized return is 9.0%. c. The analyst can conclude that the annualized return has increased. d. The analyst cannot conclude that the annualized return has increased. 2. A national survey of lawyers found that lawyers drank an average of 6.8 cups of coffee each week. A random sample of 36 stockbrokers found that the stockbrokers drank an average of 6.2 cups of coffee each week with a standard deviation of 0.5. At the 5% significance level, which of the following is most accurate? a. Stockbrokers drink the same amount of coffee per week as lawyers. b. Stockbrokers definitely drink less coffee per week than lawyers. c. The analyst cannot conclude that stockbrokers drink the same amount of coffee per week as lawyers. d. Stockbrokers drink more coffee per week than lawyers. The answer is C for both. I got them right but what confused me is in the explanation, Stalla use Z=1.65 for the 1st one and 1.96 for the 2nd one. Now I’m confused by the “5% significance level”. should the “5%” be just the alpha, or alpha/2? why did they use 90% for the 1st while using 95% for the 2nd one?
for the first one, it’s a one tailed test, so the entire rejection region is in one tail. so at 5% significance the critical value becomes 1.65 the second one is a two tailed thats why 5% is 1.96
Ah…you are absolutely right. Thank you so much for clarifying my confusion! That’s why I love this forum so much. Sometimes you get stuck and can’t get out by yourself and there are always hands reaching out to you here!
Wait a minute… I’m still confused… If it’s a two tail test, for a significant level=5%, shouldn’t each tail be alpha/2=2.5%, so we still use z=1.96 for 95%, not z=1.65 for 90%?
can u pls explain the logic behind question2. i cant figure.
H0: broker drinks an average of 6.8 cups of coffee each week Ha: not equale 6.8 I got Z calc=(6.2-6.8)/(.5/36^1/2)=-7.2 I used Z critical=1.96 for 5% significant level, 95% confidence level (Stalla used 90% Z=1.65. This is what confused me but it doesn’t affect the answer though) As -7.2 fell out the range of ±1.96, we can reject H0, which is C- The analyst cannot conclude that stockbrokers drink the same amount of coffee per week as lawyers
What about this one? I don’t think Stalla use 90% confidence level not 95% for the 2nd question is right though…