Question 1

A point estimate is a range of values used to estimate a population parameter.

Accepted Answer

A point estimate is a single value used to estimate a population parameter, not a range of values.

Question 2

A random sample of 85 group leaders and supervisors revealed that they worked an average of 6.5 years before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval for the population mean?

Accepted Answer

We can use the formula:

confidence interval = sample mean ± (z-score)(standard deviation / square root of sample size)

The z-score for a 95% confidence level is 1.96.

Plugging in the values we get:

confidence interval = 6.5 ± (1.96)(1.7 / sqrt(85))
confidence interval = 6.5 ± 0.36

Therefore, the confidence interval is (6.14, 6.86).

The answer is C.

Question 3

The test statistic for a problem involving any sample size and an unknown population standard deviation is the z distribution.

Accepted Answer

The t-distribution is used when the population standard deviation is unknown and the sample size is small.

Question 4

There are 2,000 eligible voters in a precinct. 500 of the voters are randomly selected and asked whether they planned to vote for the Democratic incumbent or the Republican challenger. Of the 500 surveyed, 350 said they would vote for the Democratic incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the Democratic incumbent?

Accepted Answer

The sample proportion is 350/500 = 0.7. Using a 0.99 confidence level, the z-score is approximately 2.576. The standard error is sqrt[(0.7)(0.3)/500]. The confidence interval is 0.7 ± 2.576 * standard error, which gives limits approximately 0.647 and 0.753.

Question 5

The population variation as measured by the standard deviation has little or no effect in determining the size of a sample selected from the population.

Accepted Answer

The population variation, as measured by the standard deviation, does have an effect on determining the size of a sample. A larger standard deviation implies more variability in the data, which requires a larger sample size to accurately represent the population. A smaller standard deviation implies less variability and thus, a smaller sample size may suffice.

Question 6

A confidence interval for a population proportion is based on using the uniform distribution to approximate the binomial distribution.

Accepted Answer

A confidence interval for a population proportion is based on using the normal distribution to approximate the binomial distribution, not the uniform distribution.

Question 7

The 95 percent confidence interval states that 95 percent of the sample means of a specified sample size selected from a population will lie within plus and minus 1.96 standard deviations of the hypothesized population mean.

Accepted Answer

This statement is true. The 95 percent confidence interval is commonly used in statistical inference to estimate the range in which a population mean is likely to fall based on a sample mean. The value 1.96 represents the number of standard deviations from the mean that encompasses 95 percent of the normal distribution.

Question 8

The mean number of travel days per year for salespeople employed by hardware distributors needs to be estimated with a 0.90 degree of confidence. For a small pilot study the mean was 150 days and the standard deviation was 14 days. If the population mean is estimated within two days, how many salespeople should be sampled?

Accepted Answer

The sample size needed to estimate the population mean within two days with a 0.90 degree of confidence is 511. This is calculated using the formula: n = (Z^2 * s^2) / e^2, where Z is the z-score for the desired confidence level, s is the sample standard deviation, and e is the margin of error. In this case, Z = 1.645 (for a 0.90 confidence level), s = 14, and e = 2. Plugging these values into the formula, we get n = (1.645^2 * 14^2) / 2^2 = 511.

Question 9

The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95 percent interval for the population mean?

Accepted Answer

The 95% confidence interval for the population mean is calculated using the formula: mean ± (Z * (σ/√n)), where Z is the Z-score for 95% confidence (1.96), σ is the population standard deviation, and n is the sample size. Plugging in the values: 15.8 ± (1.96 * (3.8/√49)) gives the interval 14.7 to 16.9.

Question 10

A point estimate is a single value used to estimate a population parameter.

Accepted Answer

A point estimate is indeed a single value used to estimate a population parameter.

Question 11

To determine the size of a sample, the standard deviation of the population must be estimated by either taking a pilot survey or by approximating it based on knowledge of the population.

Accepted Answer

To determine the size of a sample, it is necessary to estimate the standard deviation of the population. This can be done by taking a pilot survey or by approximating it based on knowledge of the population. Therefore, the statement is true.

Question 12

The proportion of junior executives leaving large manufacturing companies within three years is to be estimated within 3 percent. The 0.95 degree of confidence is to be used. A study conducted several years ago revealed that the percent of junior executives leaving within three years was 21. To update this study, the files of how many junior executives should be studied?

Accepted Answer

To determine the sample size needed, use the formula for sample size estimation for proportions: n = (Z^2 * p * (1-p)) / E^2. Here, Z is the Z-score for a 95% confidence level (1.96), p is the estimated proportion (0.21), and E is the margin of error (0.03). Plugging in these values gives n ≈ 709.

Question 13

One factor in determining the size of a sample is the degree of confidence selected. This is usually 0.95 or 0.99, but it may be any degree of confidence you specify.

Accepted Answer

This statement is true as the degree of confidence is one of the factors that affect the sample size in statistical analysis.

Question 14

A sample of 2000 union members was selected and their opinions regarding a proposed management union contract were recorded. 1,600 members were in favor of it. A 95% confidence interval for the population proportion was computed to be 0.78 and 0.82. This indicates that about 80 out of 100 similarly constructed intervals would include the population proportion.

Accepted Answer

The answer of A sample of 2000 union members was...

Question 15

The finite population correction factor is used to adjust the z-statistic.

Accepted Answer

The answer of The finite population correction factor is used...

Question 16

An interval estimate is a range of values used to estimate a population parameter.

Accepted Answer

This is true. An interval estimate provides a range of values that is likely to contain the true value of a population parameter with a certain level of confidence.

Question 17

An interval estimate is a single value used to estimate a population parameter.

Accepted Answer

An interval estimate is a range of values used to estimate a population parameter, not a single value.

Question 18

To determine the value of the standard error of the mean, the total error is divided by the sample size.

Accepted Answer

The standard error of the mean is calculated by dividing the standard deviation by the square root of the sample size, not the total error by the sample size.

Question 19

The finite population correction factor is applied when the population size is known.

Accepted Answer

The finite population correction factor is only applied when the population size is known, so that the sample size can be adjusted accordingly. If the population size is unknown or very large, the correction factor is not needed.

Question 20

The t distribution is based on the assumption that the population of interest is normal or nearly normal.

Accepted Answer

The t-distribution is used when the sample size is small and the population standard deviation is unknown, assuming the population is normal or nearly normal.

Quiz 9: Estimation and Confidence Intervals