Question

1. The mean of all the sample means is _______.

Multiple Choice

• α

• σ

• µ

• X

4. According to the central limit theorem, ____________.

Multiple Choice

• increasing the sample size decreases the dispersion of the sampling distribution

• the sampling distribution of the sample means will be skewed

• the sampling distribution of the sample means is uniform

• sample size is important when the population is not normally distributed

5. The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the probability that the mean of this sample is between 19 hours and 20 hours?

Multiple Choice

• Cannot be calculated based on the given information.

• −2.00

• 0.4772

• 2.00

9. Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes, and the population standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the probability that the mean time for the sample of 100 returns is between 88 minutes and 92 minutes?

Multiple Choice

• 0.1664

• 0.8472

• 0.8336

• Approximately 1

11. Suppose we select every fifth invoice in a file. What type of sampling is this?

Multiple Choice

• Cluster

• Systematic

• Stratified

• Random

15. The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the standard error of the mean?

Multiple Choice

• 0.50

• 6.00

• 0.25

• 2.00

Answer 1

ANSWERS:

1)

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4) According to the central limit theorem, the sampling distribution of the sample means is approximately normally distributed .

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5) c) 0.4772

The z-score is obtained as shown below:

From the information the study follows a normal distribution. The mean amount of time undergraduate student study per week is 20 hours and with a standard deviation of 6 hours. The total number of sample is 144.

The z-score for the sample mean 19 is,

The z-score for the sample mean 20 is,

The probability that the mean of the sample is between 19 and 20 is obtained as shown below:

From the information, the mean of the distribution is 20 hours and the standard deviation of the distribution is 6 hours. The total sample size is 144. The z-score obtained for the sample mean 19 is -2 and the z-score for the sample mean 20 is 0.

The required probability is,

From the “standard normal table”, the area to the left of is 0.5000 and is 0.0228.

Thus, the probability that the mean of the sample is between 19 and 20 is 0.4772.

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9) b)0.8472

= / n = 14 / 100 = 1.4

= P[(88 - 90) / 1.4 < ( - ) / < (92 - 90) / 1.4)]

= P(-1.43 < Z < 1.43)

= P(Z < 1.43) - P(Z < -1.43)

= 0.8472

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11) b) Systematic

its known as SYSTEMATIC RANDOM SAMPLING....

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15) a) 0.50

^{Standard error = standard deviation / sqt ( smple size )}

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