Question 1

When using Student's t to compute an interval estimate, ___________.
A) we assume that the samples are collected from populations that are uniformly distributed
B) we estimate the population mean based on the sample mean
C) we use the z distribution
D) we assume that the samples are collected from normally distributed populations

Accepted Answer

When using Student's t to compute an interval estimate, we assume that the samples are collected from normally distributed populations.

Question 2

Which statement(s) is/are correct about the t distribution?
A) The mean is zero.
B) Its shape is symmetric.
C) Its dispersion is based on degrees of freedom.
D) All apply.

Accepted Answer

A) The mean of the t distribution is zero.
B) The t distribution is approximately symmetric.
C) The dispersion of the t distribution is based on degrees of freedom.

Question 3

A sample mean is the best point estimate of _______.
A) the population standard deviation
B) the population median
C) the population mean
D) the sample standard deviation

Accepted Answer

A sample mean is the best point estimate of the population mean. This is because the sample mean is calculated using the sample data and provides an estimate of the true population mean. The other options (population standard deviation, population median, and sample standard deviation) are not estimated using the sample mean.

Question 4

Of the following characteristics, the t distribution and z distribution are the same in all BUT one. Which one is it?
A) Continuous
B) Symmetrical
C) Bell-shaped
D) Mean = 0, and standard deviation = 1

Accepted Answer

The t distribution has a mean of 0 but a slightly larger standard deviation than the normal distribution, as it takes into account the variability due to smaller sample sizes.

Question 5

When a confidence interval for a population mean is constructed from sample data, __________.
A) we can conclude that the population mean is in the interval
B) we can conclude that the population mean is not in the interval
C) we can conclude, for an infinite number of samples and corresponding confidence intervals, that the population mean is in a stated percentage of the intervals
D) we cannot make any inferences

Accepted Answer

The confidence interval provides a range of values that is likely to contain the population mean with a stated level of confidence. This means that for an infinite number of samples and corresponding confidence intervals, a certain percentage of those intervals will contain the population mean. Therefore, we can conclude, for these infinite intervals, that the population mean is in a stated percentage of the intervals. However, we cannot say with certainty that the population mean is in the specific interval computed from a single sample.

Question 6

A random sample of 20 items is selected from a population. When computing a confidence interval for the population mean, what number of degrees of freedom should be used to determine the appropriate t-value?
A) 20
B) 19
C) 21
D) 25

Accepted Answer

The appropriate number of degrees of freedom to use when computing a confidence interval for the population mean with a sample size of 20 is 19. This is because the degrees of freedom for a t-distribution in this case is equal to the sample size minus one. Therefore, 20-1=19.

Question 7

The distribution of Student's t has _________.
A) a mean of zero and a standard deviation of one
B) a mean of one and a standard deviation of one
C) a mean of zero and a standard deviation that depends on the sample size
D) a mean that depends on the sample size and a standard deviation of one

Accepted Answer

The distribution of Student's t has a mean of zero, but the standard deviation depends on the sample size. Specifically, it is equal to the square root of the sample size divided by the degrees of freedom (sample size minus one).

Question 8

Knowing the population standard deviation, a 95% confidence interval infers that the population mean ___________.
A) is between 0 and 100%
B) is within ±1.96 standard deviations of the sample mean
C) is within ±1.96 standard errors of the sample mean
D) is too large

Accepted Answer

The answer of Knowing the population standard deviation, a 95%...

Question 9

How is the t distribution similar to the standard z distribution?
A) Both are discrete distributions.
B) Both are skewed distributions.
C) Both are families of distributions.
D) Both are continuous distributions.

Accepted Answer

Both the t distribution and the standard z distribution are continuous distributions. However, they differ in shape and variability. The t distribution is slightly more spread out and has heavier tails than the standard z distribution.

Question 10

What kind of distribution is the t distribution?
A) Continuous
B) Discrete
C) Subjective
D) A z distribution

Accepted Answer

The t distribution is a continuous probability distribution, used for making inferences about a population mean when the sample size is small or when the population standard deviation is unknown.

Question 11

A random sample of 42 college graduates revealed that they worked an average of 5.5 years on the job before being promoted. The sample standard deviation was 1.1 years. Using the 0.99 degree of confidence, what is the confidence interval for the population mean?
A) 5.04 and 5.96
B) 5.06 and 5.94
C) 2.67 and 8.33
D) 4.40 and 6.60

Accepted Answer

The confidence interval for the population mean can be calculated using the formula: $\bar{x} \pm z\frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $z$ is the z-score corresponding to the confidence level. For a 99% confidence level, the z-score is approximately 2.58. Plugging in the given values: $5.5 \pm 2.58\frac{1.1}{\sqrt{42}}$, we get the interval $5.04$ to $5.96$.

Question 12

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The results showed that the mean tread life was 50,000 miles, with a standard deviation of 3,500 miles. What is the best estimate of the mean tread life in miles for the entire population of these tires?
A) 50,000
B) 3,500
C) 500
D) 35

Accepted Answer

The best estimate of the population mean is the sample mean, which is 50,000 miles. This is the most accurate estimate based on the information given in the problem. Option B is the standard deviation and does not give information about the mean, while options C and D are not relevant to the problem.

Question 13

Which of the following is NOT necessary to determine how large a sample to select from a population?
A) The level of confidence in estimating the population parameter
B) The size of the population
C) The maximum allowable error in estimating the population parameter
D) An estimate of the population variation

Accepted Answer

The size of the population is generally not necessary for determining sample size, especially in large populations, as sample size is more influenced by the desired confidence level, allowable error, and population variation.

Question 14

The distribution of Student's t is ________.
A) symmetrical
B) negatively skewed
C) positively skewed
D) a discrete probability distribution

Accepted Answer

The t-distribution is symmetrical around the mean, with the shape depending on the degrees of freedom.

Question 15

Which of the following is a point estimate for the population mean (µ)?
A) σ
B) x/n
C) 
D) s

Accepted Answer

The answer of Which of the following is a point...

Question 16

A sample standard deviation is the best point estimate of the ___________.
A) population range
B) population skewness
C) population mode
D) population standard deviation

Accepted Answer

A sample standard deviation is the best point estimate of the population standard deviation because it gives an estimate of the variation within the sample, which can then be used to estimate the variation within the larger population. The other options (population range, population skewness, and population mode) are not estimated by the sample standard deviation.

Question 17

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10^th of a percent)? A) 78.2% to 81.8% B) 69.2% to 86.4% C) 76.5% to 83.5% D) 77.7% to 82.3%

Accepted Answer

The answer of Suppose 1,600 of 2,000 registered voters sampled...

Question 18

What is the interpretation of a 96% confidence level?
A) There's a 96% chance that the given interval includes the true value of the population parameter.
B) Approximately 96 out of 100 such intervals would include the true value of the population parameter.
C) There's a 4% chance that the given interval does not include the true value of the population parameter.
D) The interval contains 96% of all sample means.

Accepted Answer

A 96% confidence level means that if we were to repeat our sampling process many times and construct confidence intervals for each sample, approximately 96 out of 100 of those intervals would include the true value of the population parameter. It does not mean that there is a 96% chance that the given interval includes the true value, as the true value is fixed and the interval either includes it or not. It also does not have to do with the percentage of sample means contained in the interval.

Question 19

A confidence interval for a population mean __________.
A) estimates the population range
B) estimates a likely interval for a population mean
C) estimates likelihood or probability
D) estimates the population standard deviation

Accepted Answer

A confidence interval estimates a likely interval for a population mean, with a degree of confidence. It does not estimate the population range, likelihood or probability, or the population standard deviation.

Question 20

A bank wishes to estimate the mean credit card balance owed by its customers. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and an interval of $75 is desired, how many customers should be sampled?
A) 44
B) 212
C) 629
D) 87

Accepted Answer

The answer of A bank wishes to estimate the mean...

Quiz 9: Estimation and Confidence Intervals

When using Student's t to compute an interval estimate, ___________.

Which statement(s) is/are correct about the t distribution?

A sample mean is the best point estimate of _______.

Of the following characteristics, the t distribution and z distribution are the same in all BUT one. Which one is it?

When a confidence interval for a population mean is constructed from sample data, __________.

A random sample of 20 items is selected from a population. When computing a confidence interval for the population mean, what number of degrees of freedom should be used to determine the appropriate t-value?

The distribution of Student's t has _________.

Knowing the population standard deviation, a 95% confidence interval infers that the population mean ___________.

How is the t distribution similar to the standard z distribution?

What kind of distribution is the t distribution?

A random sample of 42 college graduates revealed that they worked an average of 5.5 years on the job before being promoted. The sample standard deviation was 1.1 years. Using the 0.99 degree of confidence, what is the confidence interval for the population mean?

Which of the following is NOT necessary to determine how large a sample to select from a population?

The distribution of Student's t is ________.

Which of the following is a point estimate for the population mean (µ) ?

A sample standard deviation is the best point estimate of the ___________.

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10^th of a percent) ?

What is the interpretation of a 96% confidence level?

A confidence interval for a population mean __________.

A bank wishes to estimate the mean credit card balance owed by its customers. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and an interval of $75 is desired, how many customers should be sampled?