SOLUTION: hi, i need help with this. any kind of help will be appriciated. Question : By statistics, faculty with rank of assistant professor (AP) finishing their 2nd year of employment

Question 370409: hi, i need help with this. any kind of help will be appriciated.
Question : By statistics, faculty with rank of assistant professor (AP) finishing their 2nd year of employment at a higher education institution in Ontario earn an average of $ 68,500 per year with a standard deviation of $3500. In an attempt to verify this salary level, a random sample of 50 AP with 2 years of experiment was selected from a personnel database for all higher education institutions in Ontario.
a. Describe the sampling distribution of the sample mean �X of the average salary of these 50 AP.
b. Within what limit would you expect the sample mean to fall with probability .95
c. Calculate the probability that �X is greater than 70,000.
d. If the random sample actually produced a sample mean of 70,000, would you considerthis rather unusual? What conclusion might you draw then?
Thanks in advance.
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Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Question : By statistics, faculty with rank of assistant professor (AP) finishing their 2nd year of employment at a higher education institution in Ontario earn an average of $ 68,500 per year with a standard deviation of $3500. In an attempt to verify this salary level, a random sample of 50 AP with 2 years of experiment was selected from a personnel database for all higher education institutions in Ontario.
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a. Describe the sampling distribution of the sample mean �X of the average salary of these 50 AP.
Ans: The mean of the sample means = 68,500
The std of the sample means = 3500/sqrt(50)
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b. Within what limit would you expect the sample mean to fall with probability .95
Lower limit: x-bar = 68500-1.96* [3500/sqrt(50)] = 67529.85
Upper limit: x-bar = 68500+1.96* [3500/sqrt(50)] = 69470.15
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c. Calculate the probability that �X is greater than 70,000.
Find the t-value of 70,000
I get t = 3.0305
Find the probability that t is greater than that t-value when df = 49
I get 0.0019
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d. If the random sample actually produced a sample mean of 70,000, would you considerthis rather unusual?
Ans: Rather unusual since 70,000 is more than 3 std's above the mean.
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What conclusion might you draw then?
Ans: The population mean is probably wrong.
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Cheers,
Stan H.

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