For Questions 1 - 3, you should do the following: 1. State the null and alternat
ID: 3248507 • Letter: F
Question
For Questions 1 - 3, you should do the following:
1. State the null and alternative hypotheses.
2. Decide whether you should use the z or the t distribution.
[Hint: Even though there is not a large difference in results using the z or the t distribution when the sample size is large, sample size should not be the basis for deciding whether the z or the t distribution should be used.]
3. Show your work for the calculation of the appropriate test statistic (z or t).
4. Find the p-value of the test statistic by using Excel.
[Hint: Be careful about whether you are looking for the area above or below the test statistic value - - that would be determined by the sign (> or <) in Ha. Be especially careful if the sign in Ha is .
5. State your statistical decision (reject Ho or do not reject Ho).
6. Did you find the evidence the problem was looking for?
[Hint: Be alert! For one or more of these problems you will have to revisit work that we studied earlier this term.]
Q1. Last year, the average yield of soy beans in Iowa was 300 bushels per acre. Weather conditions were unusual this year and soy bean investors suspected that the yield would be different. A random sample of 50 plots of land selected this year had a mean yield of 311 bushels per acre. From past experience, the population standard deviation is known to be 45.4 pounds. At a significance level of .10, is there evidence that the average yield has changed?
Ho: Ha:
Should you be using z or t? (Explain.)
What is the value of the test statistic? (Show your work.)
What is the p-value?
Statistical decision:
Did you find the evidence the problem was looking for?
***Use the information in the problem to construct a 90% confidence interval estimate for the population mean. (Show work)
What is the margin of error of your estimate?
Is the H0 mean included in the confidence interval?
Explain why this is really giving you the same information as your statistical decision.
Q2. First-year lawyers in a large city earn an average of $120,000 per year. A random sample of first-year lawyers at the Dewey, Cheatum, and Howe Law Firm (where first-year salaries are known to follow a normal distribution) reported the following salaries (in thousands of dollars):
160
155
110
120
135
185
110
110
135
140
150
145
180
100
115
112
Can we conclude that the mean salary of first-year lawyers at this firm is higher than the city average? (Use = .01)
Ho: Ha:
Should you be using z or t? (Explain.)
What is the value of the test statistic? (Show your work.)
What is the p-value?
Statistical decision:
Did you find the evidence the problem was looking for?
Q3. In a random sample of 60 public college seniors, 36 of them reported that they had student loan debt exceeding $30,000. Is there evidence that more than half of public college seniors have student loan debt exceeding $30,000? (You choose the significance level.)
Ho: Ha:
Should you be using z or t? (Explain.)
What is the value of the test statistic? (Show your work.)
What is the p-value?
Statistical decision:
Did you find the evidence the problem was looking for?
Q1. Last year, the average yield of soy beans in Iowa was 300 bushels per acre. Weather conditions were unusual this year and soy bean investors suspected that the yield would be different. A random sample of 50 plots of land selected this year had a mean yield of 311 bushels per acre. From past experience, the population standard deviation is known to be 45.4 pounds. At a significance level of .10, is there evidence that the average yield has changed?
Ho: Ha:
Should you be using z or t? (Explain.)
What is the value of the test statistic? (Show your work.)
What is the p-value?
Statistical decision:
Did you find the evidence the problem was looking for?
***Use the information in the problem to construct a 90% confidence interval estimate for the population mean. (Show work)
What is the margin of error of your estimate?
Is the H0 mean included in the confidence interval?
Explain why this is really giving you the same information as your statistical decision.
Q2. First-year lawyers in a large city earn an average of $120,000 per year. A random sample of first-year lawyers at the Dewey, Cheatum, and Howe Law Firm (where first-year salaries are known to follow a normal distribution) reported the following salaries (in thousands of dollars):
160
155
110
120
135
185
110
110
135
140
150
145
180
100
115
112
Can we conclude that the mean salary of first-year lawyers at this firm is higher than the city average? (Use = .01)
Ho: Ha:
Should you be using z or t? (Explain.)
What is the value of the test statistic? (Show your work.)
What is the p-value?
Statistical decision:
Did you find the evidence the problem was looking for?
Explanation / Answer
(1) Ho: = 18000 versus Ha: 18000
(2) Since the population standard deviation is known, we can use z score
(3)
SE = /n = 45.4/50 = 6.420529573
z = (x-bar - )/SE = (18660 - 18000)/6.42052957317385 = 102.7952589
(4) p- value = 0
(5) Since 102.7952589 > 1.644853627 we reject Ho and accept Ha
(6) Yes.
Data: n = 50 = 18000 s = 45.4 x-bar = 18660Related Questions
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