1. Richard makoto Economics department University of Zimbabwe
Econ 110: Sampling Theory and Statistical Inference In Economics 2nd semester 2016
Richard makoto
Economics department
University of Zimbabwe
richard makoto university of zimbabwe

2. Sampling Theory Exercises
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3. richard makoto university of zimbabwe
A cereal packing machine is calibrated to pack a mean weight of 500g into carton boxes. There is some variation in the mean weight packed per box as measured by a standard deviation of 10g. Suppose the weight packed by the machine follows a normal distribution. What is the probability that a box will weigh
i) Less than 525g
ii) More than 480g
iii) More than 520g but less than 525g
richard makoto university of zimbabwe

4. richard makoto university of zimbabwe
The mean annual cost of automobile insurance is $939. Assume that the standard deviation is σ= $245.
What is the probability that a simple random sample of automobile insurance policies will have a sample mean within $25 of the population mean for each of the following
sample sizes: 30, 50, 100, and 400?
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5. richard makoto university of zimbabwe
The average score for male golfers is 95 and the average score for female golfers is 106. Use these values as the population means for men and women and assume that the population standard deviation is σ=14 strokes for both. A simple random sample of 30 male golfers and another simple random sample of 45 female golfers will be taken.
a. Show the sampling distribution of x-bar for male golfers.
b. What is the probability that the sample mean is within 3 strokes of the population mean for the sample of male golfers?
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6. ichard makoto university of zimbabwe
To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected.
a. Would you use the finite population correction factor in calculating the standard error of the mean? Explain.
b. If the population standard deviation is σ= 8.2 years, compute the standard error both with and without the finite population correction factor. What is the rationale for ignoring the finite population correction factor whenever n/N< .05?
c. What is the probability that the sample mean age of the employees will be within
+/-2 years of the population mean age?
ichard makoto university of zimbabwe

7. richard makoto university of zimbabwe
A simple random sample of size 100 is selected from a population with p= .40.
Show the sampling distribution of p-bar.
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8. richard makoto university of zimbabwe
The president of Doerman Distributors, Inc., believes that 30% of the firm’s orders come from first-time customers. Arandom sample of 100 orders will be used to estimate the proportion of first-time customers. a. Assume that the president is correct and p= .30. What is the sampling distribution of for this study? b. What is the probability that the sample proportion will be between .20 and .40? c. What is the probability that the sample proportion will be between .25 and .35?
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9. richard makoto university of zimbabwe
When production is operating correctly, the resistence in ohms of components produced has a normal distribution with std deviation 3.6. Arandom sample of four components was taken. What is the probability that the sample variance is bigger than 30.
richard makoto university of zimbabwe

10. Tom and George are playing in the club golf tournament
Tom and George are playing in the club golf tournament.Their scores vary as they play the course repeatedly.Tom’s score X has the N(110,10) distribution,and George’s score Y varies from round to round according to the N(100,8) distribution. If they play independently, what is the probability that Tom will score lower than George and thus do better in the tournament?
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11. Solution
The difference X −Y between their scores is Normally distributed, with mean and variance
richard makoto university of zimbabwe

12. The U.S. Department of Agriculture (USDA) uses sample surveys to produce important economic estimates. One pilot study Estimated wheat prices in July and in September using independent samples of wheat producers in the two months. Here are the summary statistics, in dollars per tonne.
Month n x-bar `s
September $3.61 `$0.19
July $2.95 $0.22
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13. Find the probability that the mean of September is greater than the mean of July.
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14. (a) Calculate the test statistic.
Here are some summary statistics from two independent samples from Normal distributions:
Sample n s2
You want to test the null hypothesis that the two population standard deviations are equal at the 5% significance level.
(a) Calculate the test statistic.
(b) Find the appropriate value from tables that You need to perform the significance test.
(c) What do you conclude?
richard makoto university of zimbabwe