Question 1

As the degrees of freedom increase, the correspondence between the t and z distributions _________.

Accepted Answer

As the degrees of freedom increase, the t-distribution approaches the normal (z) distribution, making their correspondence increase.

Question 2

The 95% confidence interval arrived at from a particular experiment is 72-79. This means that _________.

Accepted Answer

C

Question 3

The degrees of freedom for the t test for single samples are _________.

Accepted Answer

The degrees of freedom for the t test for single samples are equal to the sample size minus one (N-1). This is because one degree of freedom is lost when estimating the sample mean.

Question 4

In a correlative study, _________.

Accepted Answer

A nondirectional alternative hypothesis states that r ≠ 0, and the null hypothesis for a nondirectional alternative hypothesis states that r = 0.

Question 5

| t crit | for any alpha level is _________ | z crit | for N less than infinity.

Accepted Answer

As sample size (N) increases, z critical values approach t critical values. However, for smaller sample sizes (N less than infinity), z critical values are greater in magnitude than t critical values.

Question 6

In a t test, when the size of the sample is increased, the confidence interval _________.

Accepted Answer

When the size of the sample is increased, the confidence interval decreases because a larger sample size provides more information about the population, leading to a more precise estimate of the mean, thus narrowing the confidence interval.

Question 7

We lose one degree of freedom in calculating _________.

Accepted Answer

In calculating s and t obt for a single sample, we need to use the sample mean as an estimate of the population mean, which loses one degree of freedom. Therefore, we lose one degree of freedom for both s and t obt.

Question 8

is an estimate of _________.

Accepted Answer

The answer of  is an estimate of _________.
...

Question 9

Which of the characteristics below distinguishes the t statistic from the z statistic?

Accepted Answer

The t distribution is more spread out and has heavier tails than the normal distribution, meaning that for the same value (e.g., ±1.96), there is more area beyond that value in the t distribution compared to the normal (z) distribution. This accounts for the increased uncertainty (due to estimating the population standard deviation with the sample standard deviation) when using the t distribution.

Question 10

For a given N , the interval that bounds the population mean at the 99% confidence level is _________ that which bounds the population mean at the 95% confidence level.

Accepted Answer

The answer of For a given N , the interval...

Question 11

The df associated with evaluating the significance of r obt are _________.

Accepted Answer

The degrees of freedom associated with evaluating the significance of r obt (the observed correlation coefficient) is equal to the sample size (N) minus 2. This is because we are estimating two parameters (the slope and intercept of the regression line) from the data. Therefore, the correct answer is C, N-2.

Question 12

The confidence interval for the population mean is _________.

Accepted Answer

A confidence interval is a range of values that is likely to contain the population mean. It is not a guarantee, but rather a probability statement. Therefore, it is not a definitive range and may vary from sample to sample.

Question 13

In an independent groups experiment, if we must estimate the population standard deviation to determine the significance of the sample results, the appropriate inference test is the _________.

Accepted Answer

When the population standard deviation is not known and must be estimated from the sample data, the appropriate inference test is the t test. Both the z test and sign test assume a known population standard deviation, while the t test takes into account the uncertainty introduced by estimating the standard deviation from the sample.

Question 14

When using the t test, we reject H 0 _________.

Accepted Answer

We reject the null hypothesis (H0) when the absolute value of the observed t statistic (|tobt|) is greater than or equal to the absolute value of the critical t value (|tcrit|). This is because it indicates that the observed result is statistically significant and unlikely to have occurred by chance if the null hypothesis were true.

Question 15

The mean of the t distribution equals _________.

Accepted Answer

The t distribution is a distribution of sample means and is centered at 0. Therefore, the mean of the t distribution is also 0.

Question 16

In a correlated groups experiment, if we must estimate the population standard deviation to determine the significance of the sample results, the appropriate statistical test is _________.

Accepted Answer

The appropriate statistical test for a correlated groups experiment when estimating the population standard deviation is a t test. The t test allows us to compare the means of two related groups with unknown population standard deviations.

Question 17

As the df increases, the t distribution _________.

Accepted Answer

As the degrees of freedom (df) increase, the t distribution approaches the normal distribution. This is because the t distribution is based on smaller samples, while the normal distribution assumes an infinite sample size. As the sample size (df) for the t distribution increases, the distribution becomes more similar to the normal distribution.

Question 18

Which of the following represents a sampling distribution?

Accepted Answer

All three options (binomial, z, and t distributions) represent sampling distributions. The binomial distribution is a type of probability distribution that provides the probability of a specific number of successes in a fixed number of trials with a fixed probability of success. The z distribution is the normal distribution with a mean of 0 and a standard deviation of 1, and it is used in hypothesis testing involving z-tests. The t distribution is used in hypothesis testing involving t-tests when the sample size is small or the population standard deviation is unknown. All three distributions represent a set of outcomes that could arise from sampling repeatedly from the same population.

Question 19

The t test differs from the z test in that _________.

Accepted Answer

The t test differs from the z test in that with the t test we estimate the population standard deviation (s) instead of knowing it, and the test statistic follows a t distribution, which is a family of curves that varies depending on the sample size.

Question 20

With which statistical test do we determine the probability of getting the obtained results or those more extreme assuming the differences in results were due to chance alone?

Accepted Answer

All of these tests (sign test, z test, and t test) are used to determine the probability of obtaining the observed results, or more extreme results, under the assumption that the observed differences are due to chance alone. Each test applies to different types of data and assumptions about the data's distribution.

Quiz 13: Students T Test for Single Samples