# MATHEMATICS

1-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 39.5 and a standard deviation of 6.6.
The appropriate statistical procedure for this example would be a
A- z-test
B-t-test
2-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 39.5 and a standard deviation of 6.6.
Is this a one-tailed or a two-tailed test?
A-one-tailed
B-two-tailed
3-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 39.5 and a standard deviation of 6.6.
The most appropriate null hypothesis (in words) would be
A-There is a statistical difference in the amount of empathy expressed when comparing individuals who were bullied to the general population.
B-There is no statistical difference in the amount of empathy expressed when comparing individuals who were bullied to the general population.
C-Being bullied does significantly increase empathy when compared to the population of individuals in the general population who have not been bullied.
D-Being bullied does not significantly increase empathy when compared to the population of individuals in the general population who have not been bullied.
4-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 39.5 and a standard deviation of 6.6.
The most appropriate null hypothesis (in symbols) would be
A-μbullied = 39.5
B-μbullied = 30.6
C-μbullied > 39.5
D-μbullied > 30.6
5-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 116 scores obtained from individuals who were bullied yielded a mean of 39.5 and a standard deviation of 6.6. (Use these numbers only for this question!)
What are the degrees of freedom?
_____________________________
6-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 51.46. Random sampling of 67 scores obtained from individuals who were bullied yielded a mean of 32.05 and a standard deviation of 12.2. (Use these numbers only for this question!)
What is the z-value or t-value you obtained (your test statistic)?
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7-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 39.5 and a standard deviation of 6.6.
Test at the .05 level of significance.
The value of your calculated (obtained) test statistic is 6.74. What is your decision?
A-reject the null hypothesis
B-fail to reject the null hypothesis
C-reject the alternative hypothesis
8-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 39.5 and a standard deviation of 6.6.
Test at the .05 level of significance.
The best conclusion for this example (based on your answer to Q8) would be
A-Being bullied does not significantly increase the amount of empathy expressed by individuals who were bullied when compared to the general population.
B-Being bullied does not significantly decrease the amount of empathy expressed by individuals who were bullied when compared to the general population.
C-There is no statistical difference in the amount of empathy expressed by individuals who were bullied when compared to the general population.
D-There is a statistical difference in the amount of empathy expressed by individuals who were bullied when compared to the general population.
9-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 39.5 and a standard deviation of 6.6.
Test at the .05 level of significance.
Based on your evaluation of the null in Q8 and your conclusion is Q9, as a researcher you would be more concerned with a
A-Type I statistical error
B-Type II statistical error
10-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 74.27. Random sampling of 76 scores obtained from individuals who were bullied yielded a mean of 71.9 and a standard deviation of 22.87. (Use these numbers only for this question!)
Calculate the 99% confidence interval.
The mean you will use for this calculation is:
_____________________________________
11-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 56.01. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 62.23 and a standard deviation of 13.57. (Use these numbers only for this question!)

Calculate the 99% confidence interval.
As you know, two values will be required to complete the following equation:

_________ ≤ µ ≤ __________

For this question, what is the value that is below or less than µ?
_______________________
12-A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 56.24. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 55.11 and a standard deviation of 21.29. (Use these numbers only for this question!)
Calculate the 99% confidence interval.
Steps:
As you know, two values will be required to complete the following equation:

_________ ≤ µ ≤ __________

For this question, what is the value that is above or greater than µ?

13-If α = 0.04, and β = 0.14, complete the following questions by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this question only)
The statistical decision is to reject the null, and H0 is really true (i.e., a Type I error)
__________________________________________
14-If α = 0.13, and β = 0.2, complete the following questions by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this question only)
The statistical decision is to fail to reject null, and H0 is really true (i.e., a correct decision)
______________________________
15-If α = 0.02, and β = 0.06, complete the following questions by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this question only)
The statistical decision is to reject the null, and H0 is really false (i.e., Power)
_________________________________
16-If α = 0.1, and β = 0.05, complete the following questions by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this question only)
The statistical decision is to fail to reject the null, and H0 is really false (i.e., a Type II error)
_____________________________________
17-A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The 30 individuals who take Atenolol have an average systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure?
The appropriate statistical procedure for this example would be a:
A-t-test
B-z-test
C-chi-square goodness of fit
D-chi-square test for independence
18-A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The 30 individuals who take Atenolol have an average systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure?
Is this a one-tailed or a two-tailed test?
A-one-tailed
B-two-tailed

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