Question 1

Republicans average 1.4 children while the state as a whole averages 1.7 children. The Z score computed in this test is 0.78 and the alpha level is 0.05. Therefore, the difference in size of family________.

Accepted Answer

The Z score of 0.78 does not exceed the critical value typically associated with an alpha level of 0.05 (usually around 1.96 or -1.96 for a two-tailed test), indicating that the observed difference is not statistically significant and could be due to random chance.

Question 2

Comparing one- and two-tailed tests (with a constant alpha level and sample size), the probability of rejection will be higher for________.

Accepted Answer

In a one-tailed test, if the direction of the effect is correctly predicted, the entire alpha level is allocated to that direction, making it more likely to reject the null hypothesis compared to a two-tailed test where the alpha level is split between two directions.

Question 3

Research involving potentially harmful drugs would be likely to use an alpha level of________.

Accepted Answer

Research involving potentially harmful drugs would require a high level of significance to ensure that the drug is truly effective and not causing harm. Therefore, a very low level of alpha (e.g. 0.001) would be used to minimize the likelihood of a Type I error (rejecting the null hypothesis when it is actually true).

Question 4

In hypothesis testing, the _____________ is the critical assumption, the assumption which is actually tested.

Accepted Answer

The null hypothesis is the critical assumption which is actually tested in hypothesis testing. The research hypothesis is the alternative hypothesis which is being compared to the null hypothesis. The assumption of a normal sampling distribution and assumption that the sample was randomly selected are both important assumptions in statistical analysis, but they are not the critical assumption being tested in hypothesis testing.

Question 5

Which of the following are we unlikely to know when conducting a test of hypothesis in the one sample case?

Accepted Answer

The standard deviation of the population is typically unknown in the one sample case and must be estimated from the sample data. A, B, and D are all known or specified before conducting the test.

Question 6

In a t test of differences between means, increasing sample size will affect________.

Accepted Answer

Increasing sample size affects the degrees of freedom (since degrees of freedom are calculated based on sample size), the standard deviation of the sampling distribution (since the standard error decreases with increasing sample size), and the t score (since it is calculated using the sample mean, standard error, and sample size).

Question 7

A sample of people attending a professional football game averages 13.7 years of formal education while the surrounding community averages 12.1. The difference is significant at the .05 level. What could we conclude?

Accepted Answer

Based on the given information, we can conclude that the sample of people attending a professional football game is significantly more educated than the surrounding community as a whole. This is because the average education level of the sample is significantly higher than the average education level of the community, and the difference is statistically significant at the .05 level. Therefore, we can reject the null hypothesis and accept the research hypothesis that the sample is more educated than the community. The alpha level is not an issue in this conclusion.

Question 8

As the Critical Region decreases in size________.

Accepted Answer

As the Critical Region decreases in size, the probability of rejecting the null hypothesis when it is false (Type I error) decreases, leading to an increased probability of failing to reject the null hypothesis when it is false (Type II error).

Question 9

Given the same alpha level, the one-tailed test________.

Accepted Answer

In a one-tailed test, all of the alpha is concentrated in one direction, making it more likely to reject the Ho in that direction. Therefore, it is more likely that the Ho will be rejected compared to a two-tailed test.

Question 10

In tests of significance, if the test statistic falls in the critical region, we may conclude that________.

Accepted Answer

If the test statistic falls in the critical region, it means that the probability of obtaining that result under the null hypothesis is very low, so we reject the null hypothesis at a certain level of significance. This does not necessarily mean that the research hypothesis is true, but it indicates evidence in favor of it. The population distribution may or may not be normal and the sample size is not relevant to this decision.

Question 11

In terms of hypothesis testing, "significance" refers to the________.

Accepted Answer

Significance refers to whether the difference between the sample and population values is large enough to reject the null hypothesis. This is determined through statistical tests such as a t-test or ANOVA. Significance does not relate to differences between variables or observed and predicted outcomes.

Question 12

With alpha set at .05, the Critical Region for a two-tailed test would begin at±1.96. In a one-tailed test at the same alpha level the Critical Region would begin at________.

Accepted Answer

In a one-tailed test, the critical region is located entirely in one tail of the distribution. To find the critical value for a one-tailed test at alpha level .05, we need to divide alpha by 2 (since we are only looking at one tail) and then use a table or calculator to find the corresponding z-score. This calculation gives us a critical value of approximately 1.65. Therefore, the critical region for a one-tailed test at alpha level .05 would begin at ±1.65.

Question 13

Given that the null hypothesis is actually true, the probability of Type II error is________.

Accepted Answer

The answer of Given that the null hypothesis is actually...

Question 14

Why would researchers use the t distribution?

Accepted Answer

The t distribution is used when the population standard error is unknown, which is often the case in research studies.

Question 15

Do sex education classes and free clinics that offer counseling for teenagers reduce the number of pregnancies among teenagers? The appropriate test of this hypothesis would be________.

Accepted Answer

The answer of Do sex education classes and free clinics...

Question 16

All other things being equal, with which of the following alpha levels would we be most likely to reject the null hypothesis?

Accepted Answer

The higher the alpha level (e.g., .10), the more likely we are to reject the null hypothesis because it requires less extreme data to surpass the threshold of statistical significance.

Question 17

If we reject a null hypothesis which is in fact true, we________.

Accepted Answer

Rejecting a null hypothesis when it is actually true is the definition of a Type I error. A Type I error occurs when we reject the null hypothesis when it is true, indicating that there is a significant difference or relationship between the variables being studied when it is not the case.

Question 18

Which of the following combinations would result in a Type II error? The null hypothesis is actually _______ and our decision in Step 5 is to ________ the null hypothesis.

Accepted Answer

A Type II error occurs when the null hypothesis is false, but we fail to reject it.

Question 19

A researcher is interested in the effect that neighborhood crime-watch efforts have on the crime rate in the inner city, but he is unwilling to predict the direction of the difference. The appropriate test of hypothesis would be________.

Accepted Answer

A two-tailed test of hypothesis is appropriate when there is no clear direction of the difference between the two groups being compared. In this case, the researcher is interested in the effect of neighborhood crime-watch efforts on crime rate, but is not predicting whether it will decrease or increase the crime rate. Therefore, a two-tailed test would be appropriate to test for any significant difference between the two groups.

Question 20

If the critical region begins at Z (critical) =±2.56 and the test statistic is - 2.50, we________.

Accepted Answer

Since the test statistic of -2.50 does not fall in the critical region of ±2.56, we fail to reject the null hypothesis.

Quiz 8: Hypothesis Testing I the One Sample Case