Question 1

As the sample size becomes larger, the t distributions look ________ the z distribution.

Accepted Answer

As the sample size becomes larger, the t distribution becomes more and more similar to the standard normal distribution (z distribution), with smaller and smaller differences between the two distributions.

Question 2

The average salary for all 27 Arizona Diamondbacks in the 2012 baseball season was $2,653,029, with a standard deviation of $2,587,139.The population, all National League baseball players in 2012, earned an average salary of $3,213,479, with a standard deviation of $1,451,308.Does the average salary of the Diamondbacks players differ from that of all players in the National League? What statistical analysis is used to answer this question?

Accepted Answer

B

Question 3

A t statistic is _______ as a z statistic, making it _______.

Accepted Answer

A t statistic tends to be not as extreme as a z statistic because it accounts for the uncertainty in estimating the population standard deviation from a sample. This makes it more conservative, as it generally leads to wider confidence intervals or higher p-values compared to using a z statistic.

Question 4

If the standard deviation for a population, as estimated from a sample, is s = 6.47, then the standard error for a sample size of N = 20 is s_M =:

Accepted Answer

The standard error of the mean (SEM) is calculated by dividing the standard deviation by the square root of the sample size: SEM = s / sqrt(N). Here, s = 6.47 and N = 20, so SEM = 6.47 / sqrt(20) ≈ 1.45.

Question 5

The difference between the denominator of the z statistic and that of the single-sample t statistic is that in a:

Accepted Answer

The denominator of a z statistic is the estimated standard error (F1F1F1S1F1F1F10_M) while the denominator of a single-sample t statistic is the actual population standard error (s_M).

Question 6

A researcher collects 25 data points that yield a mean of 8.164 and a standard deviation (based on N - 1) of 2.237.What is the standard error for the distribution of means?

Accepted Answer

The formula for standard error is standard deviation divided by the square root of the sample size. 
Therefore, 
standard error = 2.237 / sqrt(25) = 0.447.

Question 7

As the sample size becomes larger, the t distributions become:

Accepted Answer

As the sample size becomes larger, the t distributions become narrower. This is because as the sample size increases, the standard error of the mean decreases, resulting in a more precise estimate of the population mean. As a result, the t distribution becomes more similar to the standard normal distribution, which is narrower and has less variation.

Question 8

The symbol representing a standard deviation calculated by using a sample to estimate the population standard deviation is:

Accepted Answer

The symbol representing a standard deviation calculated by using a sample to estimate the population standard deviation is "s". Option A ("sd") is not a valid symbol. Option B is a mix of F's and the Greek letter sigma and is not a standard symbol for standard deviation. Option D ("SD") is often used as a symbol for standard deviation, but it typically refers to the population standard deviation, which is calculated using all of the data, rather than just a sample.

Question 9

The symbol s is a _____ letter that describes a _____ statistic.

Accepted Answer

The answer of The symbol s is a _____ letter...

Question 10

As the sample size becomes smaller, the t distributions become:

Accepted Answer

As the sample size becomes smaller, the t distributions become wider. This is because smaller sample sizes have more variability and uncertainty, which results in wider t distributions.

Question 11

When the population mean but not the population standard deviation is known, which statistic is used to compare a sample to the population?

Accepted Answer

When the population mean is known but not the population standard deviation, we use a t-test to compare a sample to the population. Therefore, the best choice is D, which represents the t statistic.

Question 12

If the standard deviation for a population, as estimated from a sample, is s = 3.8, then the standard error for a sample size of N = 16 is s_M =:

Accepted Answer

The answer of If the standard deviation for a population,...

Question 13

It is known that the population mean on the math portion of the SAT is 500, with a standard deviation of 100.Assume that the average math SAT score for freshmen entering your college is 550, with a standard deviation of 110.Does the math performance of students entering your college differ from that of all individuals taking the SAT? What statistical analysis is used to answer this question?

Accepted Answer

A z test is used to compare a sample mean to a population mean when the standard deviation is known. In this case, we have the population mean and standard deviation for the math portion of the SAT, and we want to compare the sample mean (freshmen entering our college) to the population mean. A single-sample t test is used when the population standard deviation is unknown and must be estimated from the sample. A dependent-samples t test is used when comparing two sets of scores that are related (e.g. before and after treatment). Standard deviation analysis is not a specific statistical test, but rather a concept used in many different statistical analyses.

Question 14

What is the correct formula for using the sample standard deviation to estimate the population standard deviation?

Accepted Answer

The correct formula for using the sample standard deviation to estimate the population standard deviation is $\sqrt { \frac { \sum ( X - M ) ^ { 2 } } { ( N - 1 ) } }$, where $\sum ( X - M ) ^ { 2 }$ is the sum of the squared differences between each observation and the sample mean, and $N - 1$ is the sample size minus one, used for Bessel's correction.

Question 15

Why does one divide by N - 1 rather than by N when estimating a population standard deviation from the sample standard deviation?

Accepted Answer

Dividing by N - 1 instead of N corrects for the bias in the sample standard deviation and makes it an unbiased estimator of the population standard deviation. This is necessary because the sample standard deviation is likely to be an imprecise estimate, and dividing by N - 1 allows for a larger margin of error in the estimate.

Question 16

The following data were collected from a veterinarian's office over the course of a day to assess the average weight of dogs (in pounds): 10, 5, 17, 22, 50, 32, 38, and 29.What is the standard deviation for these data, first without the correction and then with the correction used when estimating a population?

Accepted Answer

The standard deviation without correction (sample standard deviation) is 13.95, and with correction (population standard deviation) is 14.91.

Question 17

What is the correct formula for calculating the standard deviation of a sample when one is NOT trying to estimate the population standard deviation?

Accepted Answer

The answer of What is the correct formula for calculating...

Question 18

The standard deviation of a distribution of scores in a sample is known as _____, while the standard deviation of a distribution of means is referred to as _____.

Accepted Answer

The standard deviation of a distribution of scores in a sample is denoted by "s" and the standard deviation of a distribution of means is denoted by "s_M". Thus, option C correctly represents these notations. Option A and D have incorrect notations for the standard deviations. Option B has "F1" and "F1F1F10" which are not valid notations for standard deviations.

Question 19

A researcher collects 25 data points that yield a mean of 8.164 and a standard deviation (based on N - 1) of 2.237.If the researcher is comparing the sample to a population mean of 9.2, what is the value of the test statistic?

Accepted Answer

The answer of A researcher collects 25 data points that...

Question 20

What is the formula for the single-sample t statistic?

Accepted Answer

The formula for the single-sample t statistic is $\frac { \left( M - \mu _ { M } \right) } { s _ { M } }$, where $M$ is the sample mean, $\mu_{M}$ is the population mean, and $s_{M}$ is the standard error of the mean.

Quiz 9: The Single-Sample T Test

As the sample size becomes larger, the t distributions look ________ the z distribution.

A t statistic is _ as a z statistic, making it _.

If the standard deviation for a population, as estimated from a sample, is s = 6.47, then the standard error for a sample size of N = 20 is s_M =:

The difference between the denominator of the z statistic and that of the single-sample t statistic is that in a:

A researcher collects 25 data points that yield a mean of 8.164 and a standard deviation (based on N - 1) of 2.237.What is the standard error for the distribution of means?

As the sample size becomes larger, the t distributions become:

The symbol representing a standard deviation calculated by using a sample to estimate the population standard deviation is:

The symbol s is a _ letter that describes a _ statistic.

As the sample size becomes smaller, the t distributions become:

When the population mean but not the population standard deviation is known, which statistic is used to compare a sample to the population?

If the standard deviation for a population, as estimated from a sample, is s = 3.8, then the standard error for a sample size of N = 16 is s_M =:

What is the correct formula for using the sample standard deviation to estimate the population standard deviation?

Why does one divide by N - 1 rather than by N when estimating a population standard deviation from the sample standard deviation?

What is the correct formula for calculating the standard deviation of a sample when one is NOT trying to estimate the population standard deviation?

The standard deviation of a distribution of scores in a sample is known as _, while the standard deviation of a distribution of means is referred to as _.

A researcher collects 25 data points that yield a mean of 8.164 and a standard deviation (based on N - 1) of 2.237.If the researcher is comparing the sample to a population mean of 9.2, what is the value of the test statistic?

What is the formula for the single-sample t statistic?

Quiz 9: The Single-Sample T Test

As the sample size becomes larger, the t distributions look ________ the z distribution.

A t statistic is _______ as a z statistic, making it _______.

If the standard deviation for a population, as estimated from a sample, is s = 6.47, then the standard error for a sample size of N = 20 is sM =:

The difference between the denominator of the z statistic and that of the single-sample t statistic is that in a:

A researcher collects 25 data points that yield a mean of 8.164 and a standard deviation (based on N - 1) of 2.237.What is the standard error for the distribution of means?

As the sample size becomes larger, the t distributions become:

The symbol representing a standard deviation calculated by using a sample to estimate the population standard deviation is:

The symbol s is a _____ letter that describes a _____ statistic.

As the sample size becomes smaller, the t distributions become:

When the population mean but not the population standard deviation is known, which statistic is used to compare a sample to the population?

If the standard deviation for a population, as estimated from a sample, is s = 3.8, then the standard error for a sample size of N = 16 is sM =:

What is the correct formula for using the sample standard deviation to estimate the population standard deviation?

Why does one divide by N - 1 rather than by N when estimating a population standard deviation from the sample standard deviation?

What is the correct formula for calculating the standard deviation of a sample when one is NOT trying to estimate the population standard deviation?

The standard deviation of a distribution of scores in a sample is known as _____, while the standard deviation of a distribution of means is referred to as _____.

A researcher collects 25 data points that yield a mean of 8.164 and a standard deviation (based on N - 1) of 2.237.If the researcher is comparing the sample to a population mean of 9.2, what is the value of the test statistic?

What is the formula for the single-sample t statistic?

A t statistic is _ as a z statistic, making it _.

If the standard deviation for a population, as estimated from a sample, is s = 6.47, then the standard error for a sample size of N = 20 is s_M =:

The symbol s is a _ letter that describes a _ statistic.

If the standard deviation for a population, as estimated from a sample, is s = 3.8, then the standard error for a sample size of N = 16 is s_M =:

The standard deviation of a distribution of scores in a sample is known as _, while the standard deviation of a distribution of means is referred to as _.