Question 1

If H0 is true and it is not rejected, then has occurred.
A)a Type I error
B)a Type II error
C)either a Type I or a Type II error
D)a correct decision

Accepted Answer

If H0 is true and it is not rejected, then it means the null hypothesis is accepted. This is a correct decision, as the null hypothesis should be accepted when it is true. Therefore, it is not a Type I or Type II error.

Question 2

If the result of a statistical test is reported as p > .05, then it indicates that the investigator .
A)failed to reject H0
B)failed to reject H1
C)accepted H1
D)rejected H0

Accepted Answer

A result of p > .05 means that the p-value is greater than the level of significance (usually .05). Therefore, the null hypothesis (H0) cannot be rejected, and there is not enough evidence to support the alternative hypothesis (H1). Thus, the investigator failed to reject H0.

Question 3

Alpha is the probability of.
A)rejecting H0 when it is true
B)failing to reject H0 when it is false
C)accepting H1 when it is true
D)rejecting H1 when it is true

Accepted Answer

Alpha is the level of significance, which is the maximum probability of rejecting the null hypothesis when it is actually true. This means that if we set alpha at 0.05, there is a 5% chance of rejecting the null hypothesis even if it is true.

Question 4

Underlying the use of the one-sample t test is the assumption that the.
A)distribution of scores in the sample is symmetrical
B)population variance is equal to the sample variance
C)degrees of freedom are greater than 30
D)scores in the population are normally distributed

Accepted Answer

The one-sample t test assumes that scores in the population are normally distributed, as this is a key assumption for using the t distribution.

Question 5

If the result of a one-sample t test is reported as t(49) = 2.329, p < .05, then you know that.
A)the critical value of t was 2.329
B)the alpha level was less than .05
C)the sample size was 49
D)none of the above

Accepted Answer

The sample size is actually 50, as the degrees of freedom (49) is one less than the sample size. The critical value is not necessarily 2.329, and the alpha level is typically set at .05, not less.

Question 6

A nonsignificant difference is attributed to.
A)the effects of stratified sampling
B)an insufficiently low alpha value
C)sampling error
D)a standard error

Accepted Answer

A nonsignificant difference between two groups or conditions is often attributed to chance variability, or sampling error. This means that the difference between the groups may not be statistically significant, but it could still be meaningful or important in other ways. The other answer choices (stratified sampling, alpha value, standard error) do not directly relate to whether or not a difference is significant.

Question 7

If the result of a one-sample t test is reported as p > .05, then you know that the.
A)null hypothesis was rejected
B)null hypothesis was not rejected
C)alternative hypothesis was accepted
D)probability of a Type II error was .05

Accepted Answer

If the result of a one-sample t test is reported as p > .05, it means that the obtained p-value is greater than the chosen alpha level (usually .05), which is not statistically significant. Therefore, we fail to reject the null hypothesis and accept the null hypothesis as the most likely explanation. Hence, the correct choice is B.

Question 8

If the observed difference between the sample mean and the hypothesized population mean in a one-sample t test is nonsignificant, then.
A)the null hypothesis was rejected
B)the null hypothesis was not rejected
C)it implies that a Type I error was made
D)the probability that a Type II error was made is equal to .05

Accepted Answer

If the observed difference between the sample mean and the hypothesized population mean is nonsignificant, it means that the null hypothesis cannot be rejected, which is the correct conclusion for a one-sample t test. A nonsignificant result does not necessarily mean a Type I error was made, and it also does not provide information about the probability of a Type II error.

Question 9

A Type I error occurs if the null hypothesis is when it is.
A)rejected; true
B)not rejected; true
C)rejected; false
D)not rejected; false

Accepted Answer

A Type I error occurs when the null hypothesis is rejected even though it is true.

Question 10

The use of the one-sample t test rests on the assumption that the sample.
A)is symmetrical
B)was randomly selected from the population
C)variance is known
D)standard deviation is known

Accepted Answer

The one-sample t test assumes that the sample was randomly selected from the population, which allows for unbiased estimates of the population parameters. The test does not assume that the sample is symmetrical or that the variance or standard deviation is known.

Question 11

If the null hypothesis is not rejected in a one-sample t test, then the.
A)sample mean and the population mean differ significantly from each other
B)alpha level should be increased
C)observed difference between the sample mean and the population mean is attributed to sampling error
D)distributions of scores within both the sample and the population are normal

Accepted Answer

If the null hypothesis is not rejected in a one-sample t test, it means that the observed difference between the sample mean and the population mean is not significant enough to conclude that they are different from each other. This lack of significance is attributed to sampling error, which suggests that the sample is a representative of the population. Therefore, the null hypothesis is accepted, and there is no need to increase the alpha level. Normality is not a requirement for the null hypothesis not to be rejected, although it is important for conducting a t test.

Question 12

If tobs falls into a rejection region, then which of the following is true?
A)The probability of obtaining the value of tobs under the null hypothesis is greater than the alpha value.
B)The alternative hypothesis is not accepted.
C)The null hypothesis is rejected.
D)The null hypothesis is not rejected.

Accepted Answer

If tobs falls into a rejection region, it means that the calculated test statistic is unlikely to have occurred by chance alone and therefore falls into the critical region. This leads to the rejection of the null hypothesis in favor of the alternative hypothesis.

Question 13

If the result of a statistical test is reported as p < .05, then it indicates that the investigator .
A)failed to reject H0
B)failed to reject H1
C)rejected H1
D)rejected H0

Accepted Answer

When p < .05, it means that there is less than a 5% chance that the results occurred by chance alone, so the null hypothesis (H0) is rejected in favor of the alternative hypothesis (H1). Therefore, the correct answer is D, which indicates that the investigator rejected H0.

Question 14

If the alternative hypothesis is true and H0 is not rejected, then.
A)a Type I error has occurred
B)a Type II error has occurred
C)a correct decision has occurred
D)it is possible that both a Type I and Type II error have occurred

Accepted Answer

If the alternative hypothesis is true and H0 is not rejected, then it means that a Type II error has occurred, which is the acceptance of a false null hypothesis.

Question 15

If the results of a study using the one-sample t test were summarized t(14) = 3.218, p < .01, then you would know that the probability of tobs if H0 is true is and that the difference between X and μ is. 
A)less than or equal to .01; nonsignificant
B)less than or equal to.01; statistically significant
C)greater than .01; nonsignificant
D)greater than .01; statistically significant

Accepted Answer

The result t(14) = 3.218 indicates that the t-value calculated from the sample is 3.218 standard errors away from the mean. The p-value < .01 indicates that the probability of getting a t-value as large as 3.218 (or larger) if the null hypothesis is true is less than .01. This means that the results are statistically significant at the .01 level of significance, providing evidence against the null hypothesis. Therefore, the answer is B, less than or equal to .01 and statistically significant.

Question 16

If a(n) hypothesis is rejected when it was in fact true, then a error has occurred.
A)null; Type I
B)alternative; Type I
C)null; Type II
D)alternative; Type II

Accepted Answer

This statement describes a Type I error, which occurs when a null hypothesis is rejected even though it is true.

Question 17

If tobs does not fall into a rejection region, then which of the following is true?
A)The probability of obtaining the value of tobs under the null hypothesis is less than the alpha value.
B)The alternative hypothesis is accepted.
C)The null hypothesis is rejected.
D)The null hypothesis is not rejected.

Accepted Answer

If tobs does not fall into a rejection region, we fail to reject the null hypothesis. Therefore, choice D is true -- the null hypothesis is not rejected.

Question 18

If the results of a study using the one-sample t test were summarized t(99) = 1.546, p > .05, then you would know that the sample size was and the null hypothesis was
)
A)99; rejected
B)99; not rejected
C)100; rejected
D)100; not rejected

Accepted Answer

The sample size is indicated by the number in parentheses after the t value, which is 99 in this case. The p-value is greater than .05, which means we fail to reject the null hypothesis. Therefore, the null hypothesis is not rejected and the sample size was 100.

Question 19

You make a Type II error when you.
A)reject H0 when it is true and H1 is false
B)accept H1 when it is true and H0 is false
C)fail to reject H0 when it is false and H1 is true
D)fail to reject H1 when it is false and H0 is true

Accepted Answer

A Type II error occurs when H0 is false and H1 is true, but we fail to reject H0. This means that we incorrectly conclude that there is not enough evidence to reject the null hypothesis and accept that there is no significant difference, when in reality there is a significant difference.

Question 20

If a(n) hypothesis is not rejected when in fact it is true, then error has occurred.
A)null; no
B)null; a Type I
C)alternative; no
D)alternative; a Type II

Accepted Answer

When a null hypothesis is not rejected and it is in fact true, no error has occurred because the correct decision has been made.

Quiz 8: Is There Really a Difference Introduction to Statistical Hypothesis Testing

If H0 is true and it is not rejected, then has occurred.

If the result of a statistical test is reported as p > .05, then it indicates that the investigator .

Alpha is the probability of.

Underlying the use of the one-sample t test is the assumption that the.

If the result of a one-sample t test is reported as t(49) = 2.329, p < .05, then you know that.

A nonsignificant difference is attributed to.

If the result of a one-sample t test is reported as p > .05, then you know that the.

If the observed difference between the sample mean and the hypothesized population mean in a one-sample t test is nonsignificant, then.

A Type I error occurs if the null hypothesis is when it is.

The use of the one-sample t test rests on the assumption that the sample.

If the null hypothesis is not rejected in a one-sample t test, then the.

If tobs falls into a rejection region, then which of the following is true?

If the result of a statistical test is reported as p < .05, then it indicates that the investigator .

If the alternative hypothesis is true and H0 is not rejected, then.

If the results of a study using the one-sample t test were summarized t(14) = 3.218, p < .01, then you would know that the probability of tobs if H0 is true is and that the difference between X and μ is.

If a(n) hypothesis is rejected when it was in fact true, then a error has occurred.

If tobs does not fall into a rejection region, then which of the following is true?

If the results of a study using the one-sample t test were summarized t(99) = 1.546, p > .05, then you would know that the sample size was and the null hypothesis was )

You make a Type II error when you.

If a(n) hypothesis is not rejected when in fact it is true, then error has occurred.