Q: On-Line Coupons, Inc. finds that 18% of a sample of 500 coupons were not used, while the population nonuse rate is 15%. What is the z-value for this sample proportion?

$$z = \frac{0.18 - 0.15}{\sqrt{\frac{0.15 \times 0.85}{500}}} = 1.88$$

Question 1

Which of the following best defines 'sampling error' in the context of business statistics?

Accepted Answer

The difference between a measure computed from a sample (a statistic) and the corresponding measure computed from the population (a parameter).

Question 2

A company has a population mean office complex size of 158,972 square feet. A random sample of 5 complexes has a mean of 155,072 square feet. What is the sampling error for this sample?

Accepted Answer

$$155,072 - 158,972 = -3,900$$ square feet

Question 3

Which of the following statements about sample size and sampling error is TRUE?

Accepted Answer

Larger sample sizes tend to reduce the average sampling error, but do not guarantee a smaller sampling error for every sample.

Question 4

What is a 'simple random sample'?

Accepted Answer

A sample selected in such a manner that each possible sample of a given size has an equal chance of being selected.

Question 5

If the population standard deviation is $$\sigma = 1.503$$ and the sample size is $$n = 10$$, what is the standard error of the sample mean?

Accepted Answer

$$\frac{1.503}{\sqrt{10}}$$

Question 6

According to the Central Limit Theorem, what happens to the sampling distribution of the sample mean as the sample size increases?

Accepted Answer

It becomes approximately normal, regardless of the shape of the population distribution.

Question 7

A population is right-skewed with mean $$\mu = 12.50$$ and standard deviation $$\sigma = 5.50. If a $$sample of $$n = 100 is $$taken, what is the standard error of the mean?

Accepted Answer

$$\frac{5.50}{\sqrt{100}} = 0.55$$

Question 8

Which of the following is an unbiased estimator of the population mean?

Accepted Answer

The sample mean $$\bar{x}$$

Question 9

A quality analyst samples 8 tiles from a production process with $$\mu = 1.5$$ inches and $$\sigma = 0.05$$ inches. The sample mean is $$1.565$$ inches. What is the z-value for this sample mean?

Accepted Answer

$$z = \frac{1.565 - 1.5}{0.05/\sqrt{8}} = 3.67$$

Question 10

Which of the following conditions must be met to use the normal approximation for the sampling distribution of a sample proportion?

Accepted Answer

$$np \geq 5$$ and $$n(1-p) \geq 5$$

Question 11

A health clinic has a population of 80 patients, 72 of whom are satisfied with their service. What is the population proportion of satisfied patients?

Accepted Answer

$$p = \frac{72}{80} = 0.90$$

Question 12

If a sample of 20 patients is selected from the clinic, and 12 are satisfied, what is the sample proportion?

Accepted Answer

$$\hat{p} = \frac{12}{20} = 0.60$$

Question 13

On-Line Coupons, Inc. finds that 18% of a sample of 500 coupons were not used, while the population nonuse rate is 15%. What is the z-value for this sample proportion?

Accepted Answer

$$z = \frac{0.18 - 0.15}{\sqrt{\frac{0.15 	imes 0.85}{500}}} = 1.88$$

Question 14

Which of the following best describes the Central Limit Theorem?

Accepted Answer

For sufficiently large sample sizes, the distribution of the sample means is approximately normal, regardless of the population distribution.

Question 15

A statistic is said to be a 'consistent estimator' of a parameter if:

Accepted Answer

As the sample size increases, the statistic tends to get closer to the parameter.

Question 16

If the population mean is $$\mu$$ and the population standard deviation is $$\sigma$$, what is the mean and standard deviation of the sampling distribution of the sample mean for samples of size $$n$$?

Accepted Answer

Mean: $$\mu$$, Standard deviation: $$\frac{\sigma}{\sqrt{n}}$$

Question 17

A sample mean is 2.41, the population mean is 2.505, and the standard error is 0.421. What is the z-value for this sample mean?

Accepted Answer

$$z = \frac{2.41 - 2.505}{0.421} = -0.23$$

Question 18

Which of the following is NOT a property of the sampling distribution of the sample mean?

Accepted Answer

The sampling distribution always has the same shape as the population distribution, regardless of sample size.

Chapter 7: Introduction to Sampling Distributions – Business Statistics Study Notes

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