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Business statistics I Practice Test 5 (Chapter 7 & 8) 1
Business statistics I
Practice Test 5 (Chapter 7 & 8)
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1. From a population containing 5 items (A, B, C, D, and E), all possible samples of size 2 (n=2) are to be drawn.
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2.
Assume a finite population contains 95 items. Use a random number table to draw a random sample of size 15.
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3. The following sample data indicate the number of days absent for 6 employees in a company: 5, 8, 10, 7, 10, 14
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4. Suppose that the mean of a population is 200 with a standard deviation of 50. A simple random sample of size 100 (n=100) is selected from this population. The sample mean x will be used to estimate the population mean μ.
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5.
Describe the central limit theorem. What is the importance of this theorem in sampling distribution?
6.
The mean price of a particular brand of a digital camera is $200, with a standard deviation of $50. Suppose these values are the population mean and standard deviation for this brand of camera; that is, μ = 200 and s =
50. From this population, a random sample of size 100 (n=100) is selected to estimate the population mean price, μ.
- Find the probability that the sample mean will be within ± 5 of the population mean, or the probability that the sample mean x is between $195 and $205?
- Find the probability that the sample mean will be within ± 10 of the population mean, or the probability that the sample mean x is between $190 and $210?
7.
Suppose you draw a sample of size 50 from a population with a standard deviation of 10 (σ = 10). Find the standard error of the mean if (a) the population is infinite (b) the population size is N=50,000, (c) N= 5000, (d) N=500. Comment on your results.
8.
The mean annual starting salary for the accounting major was $30, 393 with a standard deviation of $2000. Suppose this value holds for the population of graduates with accounting majors; that is, ? = $30,393 and the standard deviation, σ = $2,000. Find the probability that the sample mean salary will be within ±250 of the population mean if you select a random sample of 30, 50, 100, 200, and 400? What happens to the probability values as the sample size was increased? Would you prefer a large sample to estimate the population mean? Why?
9.
Suppose the population proportion (p) of a population is 0.4 (p=0.40). A simple random sample of 100 is selected from this population. (a) What is the expected value of p ?
- What is the standard deviation of p ?
- What is the sampling distribution of p , or what distribution would the sample proportion p follow?
- Draw a sketch and show the sampling distribution of sample proportion, p .
10.
Suppose that a prime?time show of Fox TV network is watched by 40% of the audience in a city. You select a random sample of 200 viewers so that the sample proportion p can be used to estimate the population proportion, p.
- Find the probability the sample proportion will be within 3% or ±0.03 of the population proportion?
- Find the probability the sample proportion will be within 5% or ±0.05 of the population proportion?
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11. A sample of size 50 was drawn from a population with a known ?. The sample mean was found to be 32. Suppose that the population standard deviation, ?=6.
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12. The following are the scores on IQ tests of a sample of 20 students at a university: 120 118 119 132 135 122 118 139 140 128 125 115 135 139 130 112 129 140 115 120
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13. A simple random sample of 20 machining jobs indicated the average processing time of 17.25 minutes with a sample standard deviation of 3.3 minutes.
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14. An analyst wants to determine the mean salary of recent graduates in Mechanical Engineering. The margin of error in estimating the mean is to be within $500 with a 95% level of confidence. The analyst found a report by the Department of Labor that estimated the standard deviation to be $2000.
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15. Out of a random sample of 814 individuals working in a city, 562 indicated that they were satisfied with their working condition.
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16. A recent survey about the state of economy by a news media indicated that approximately 35% of the population believed that the economy is improving. It was felt that the sample size used for this study was too small and the margin of error was too large.
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