Question 1

When N > 40,and the raw scores in the population are normally distributed,then the normal and t distributions are very different from one another.

Accepted Answer

When N > 40, the t-distribution closely approximates the normal distribution, making them very similar.

Question 2

If an observed z or t score is greater than the critical value,we would reject the null hypothesis.

Accepted Answer

This is true for both z-tests and t-tests. The critical value represents the cutoff point for the level of significance chosen for the hypothesis test (usually p < .05). If the observed z or t score exceeds the critical value, the result is statistically significant and we reject the null hypothesis.

Question 3

The confidence interval most commonly used by researchers in the behavioral sciences is the 100% confidence interval.

Accepted Answer

The most commonly used confidence interval in the behavioral sciences is actually the 95% confidence interval. This means that researchers are 95% confident that the true population parameter falls within the bounds of the calculated interval.

Question 4

Confidence intervals are calculated around the observed sample mean rather than ì.

Accepted Answer

Confidence intervals are calculated around the observed sample mean as it provides an estimate of the true population mean. The true population mean (ì) is not known and hence, it cannot be used in the calculation of confidence intervals.

Question 5

The null hypothesis is the hypothesis that is assumed to be true in statistical hypothesis testing.

Accepted Answer

The null hypothesis is always assumed to be true in statistical hypothesis testing until proven otherwise by the alternative hypothesis.

Question 6

A t value is analogous to a z score except that it represents the number of estimated standard errors a sample mean is from ì.

Accepted Answer

This is true. While a z-score is based on a known population mean and standard deviation, a t-value is based on an estimated standard error of the mean and degrees of freedom.

Question 7

Assume that you are comparing a sample value to a population value of 75.The non-directional alternative hypothesis would be stated as ____________________.

Accepted Answer

The answer of Assume that you are comparing a sample...

Question 8

The hypothesis of "no difference" that is assumed to be true is called the ____________________.

Accepted Answer

The answer of The hypothesis of "no difference" that is...

Question 9

The alpha level reflects the probability of making a Type II error.

Accepted Answer

The alpha level reflects the probability of making a Type I error (rejecting a true null hypothesis). The probability of making a Type II error (failing to reject a false null hypothesis) is represented by the beta level.

Question 10

The t distribution is similar to the normal distribution in that it is bell shaped,unimodal,and symmetrical.

Accepted Answer

The answer of The t distribution is similar to the...

Question 11

When a researcher knows the population standard deviation,and has a population value to compare a sample value to,the appropriate statistical test is the ____________________.

Accepted Answer

The answer of When a researcher knows the population standard...

Question 12

The Publication Manual of the American Psychological Association refers to reporting confidence intervals as the "best reporting strategy" when they are relevant to the statistical test.

Accepted Answer

The APA Publication Manual recommends reporting confidence intervals as the "best reporting strategy" when they are relevant to the statistical test, as they provide important information about the precision and variability of the data.

Question 13

Statisticians have discovered that the one-sample t test is not robust to violations of the normality assumption under any conditions.

Accepted Answer

The one-sample t test is actually quite robust to violations of the normality assumption, as long as the sample size is large enough (typically at least 30). In fact, even with smaller sample sizes, the t test can still perform reasonably well if the data are not highly skewed or have extreme outliers. However, there are alternative tests (e.g. Wilcoxon signed-rank test) that are more appropriate for non-normal data.

Question 14

In general,a directional test will always be more powerful than a corresponding nondirectional test if the actual population mean and the hypothesized population mean differ in the specified direction.

Accepted Answer

This is true because with a directional test, all the rejection region is in one tail of the distribution, which makes it more focused and concentrated. Therefore, if the true population mean is in the specified direction, it is more likely to fall in the rejection region, leading to a higher chance of rejecting the null hypothesis. In contrast, a nondirectional test has a rejection region on both tails of the distribution, which spreads out the critical values and reduces the power of the test. Therefore, a directional test is preferred when we have a specific expectation about the direction of the effect.

Question 15

The robustness of a test is influenced by several factors,including sample size,the degree of violation,and the form of violation.

Accepted Answer

The robustness of a test is influenced by these factors and therefore, the statement is true.

Question 16

When the sample size is less than 40,the z and the t distributions are almost identical.

Accepted Answer

When the sample size is less than 40, the t distribution is more appropriate to use instead of the normal distribution since the sample size is too small for the standard deviation to be accurately estimated. The t distribution has heavier tails and flatter in the center compared to the normal distribution. Therefore, the z and t distributions are not almost identical.

Question 17

When a result of a statistical test is found to fall within the range of the critical values,the statistical conclusion is to ____________________.the null hypothesis.

Accepted Answer

The answer of When a result of a statistical test...

Question 18

As with the normal distribution,there is a single t distribution for every sample size.

Accepted Answer

The t-distribution varies with the degrees of freedom, which are related to the sample size. Each sample size has its own t-distribution.

Question 19

In the sampling distribution of the mean for the z distribution,95% of all sample means will fall between ____________________ standard errors from the mean.

Accepted Answer

The answer of In the sampling distribution of the mean...

Question 20

The one-sample t test is based on the assumption that the scores on the variable are normally distributed in the population.

Accepted Answer

The one-sample t test assumes that the scores on the variable are normally distributed in the population.

Quiz 8: Hypothesis Testing: Inferences About a Single Mean