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## Statistics

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 problemnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 70 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 problem!)

Test at the .05 level of significance.

Summarize the data into the appropriate test statistic.

What are the degrees of freedom? (numeric value only)

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 problemnaire designed to measure empathy, the mean score for the general population is 39.14. Random sampling of 86 scores obtained from individuals who were bullied yielded a mean of 31.7 and a standard deviation of 10.13. (Use these numbers only for this problem!)

Test at the .05 level of significance.

Summarize the data into the appropriate test statistic.

What is the z-value or t-value you obtained (your test statistic)?  (numeric value only, including negative sign if required)

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 problemnaire 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 find outd (obtained) test statistic is 6.74. What is your decision?

• reject the null hypothesis

• fail to reject the null hypothesis

• reject the alternative hypothesis

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 problemnaire 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 ex (based on your answer to Q3) would be

• Being bullied does not significantly increase the amount of empathy expressed by individuals who were bullied when compared to the general population.

• Being bullied does not significantly decrease the amount of empathy expressed by individuals who were bullied when compared to the general population.

• There is no statistical difference in the amount of empathy expressed by individuals who were bullied when compared to the general population.

• There is a statistical difference in the amount of empathy expressed by individuals who were bullied when compared to the general population.

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 problemnaire 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 Q3 and your conclusion is Q4, as a researcher you would be more concerned with a

• Type I statistical error

• Type II statistical error

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 problemnaire designed to measure empathy, the mean score for the general population is 64.31. Random sampling of 76 scores obtained from individuals who were bullied yielded a mean of 73.93 and a standard deviation of 22.87. (Use these numbers only for this problem!)

find out the 99% confidence interval.

The mean you will use for this calculation is

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 problemnaire 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.

find out the 99% confidence interval.

What is the new critical value you will use for this calculation?

• ±1.645

• ±2.064

• ±2.756

• ±2.797

• 6.74

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 problemnaire designed to measure empathy, the mean score for the general population is 51.22. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 35.91 and a standard deviation of 12.58. (Use these numbers only for this problem!)

find out the 99% confidence interval.

As you know, two values will be required to complete the following equation:

_________ ≤ µ ≤ __________

For this problem, what is the value that is below or less than µ?

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 problemnaire designed to measure empathy, the mean score for the general population is 68.71. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 32.76 and a standard deviation of 6.11. (Use these numbers only for this problem!)

find out the 99% confidence interval.

As you know, two values will be required to complete the following equation:

_________ ≤ µ ≤ __________

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

10) If α = 0.16, and β = 0.22, complete the following problems by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this problem only)

The statistical decision is to reject the null, and H0 is really true (i.e., a Type I error)

11) If α = 0.16, and β = 0.08, complete the following problems by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this problem only)

The statistical decision is to fail to reject null, and H0 is really true (i.e., a correct decision)

12) If α = 0.13, and β = 0.15, complete the following problems by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this problem only)

The statistical decision is to reject the null, and H0 is really false (i.e., Power)

13) If α = 0.13, and β = 0.08, complete the following problems by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this problem only)

The statistical decision is to fail to reject the null, and H0 is really false (i.e., a Type II error)

14) 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? Set alpha equal to .01.

Set up the criteria for making a decision. That is, find the critical value using an alpha = .01.  (Make sure you are sign specific: + ; - ; or +/-) (Use your tables)

• +/- 2.457

• - 2.462

• - 2.750

• +/- 2.756

15) 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 43 individuals who take Atenolol have an average systolic blood pressure of 147, with a sample standard deviation of 15.35. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure?  (Use these numbers only for this problem!)

What is the numeric value of your standard error?

16) 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 140 (µ = 140). The 167 individuals who take Atenolol have an average systolic blood pressure of 151, 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?  (Use these numbers only for this problem!)

What is the z-value or t-value you obtained (your test statistic)?  (numeric value only, including negative sign if required)

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? Set alpha equal to .01.

The value of your find outd (obtained) test statistic is -16.51. What is your decision?

• Reject the null hypothesis

• Fail to reject the null hypothesis

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? Set alpha equal to .01.

The best conclusion for this ex (based on your answer to Q17) would be:

• There is no significant difference in systolic blood pressure when comparing people who take Atenolol to the general population of people who do not take Atenolol.

• There is a significant difference in systolic blood pressure when comparing people who take Atenolol to the general population of people who do not take Atenolol.

• People taking Atenolol did not experience a significantly lower systolic blood pressure when compared to the general population of people who do not take Atenolol.

• People taking Atenolol experienced a significantly lower systolic blood pressure when compared to the general population of people who do not take Atenolol.

19)  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? Set alpha equal to .01.

Based on whether you rejected or failed to reject the null hypothesis (Q17), and your conclusion in Q18, as a researcher, you would be more concerned with a:

• Type I statistical error

• Type II statistical error

20) 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 118, 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? (Use these data for this problem only!)

find out the 95% confidence interval.

The mean you will use for this calculation is:

21) 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?

find out the 95% confidence interval.

What is the new critical value you will use for this calculation?

• +/- 1.699
• +/- 2.045
• +/- 2.457
• +/- 2.462
• - 2.045

22)  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 167 (µ = 167). The 30 individuals who take Atenolol have an average systolic blood pressure of 150, with a sample standard deviation of 25. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this problem!)

find out the 95% confidence interval.

As you know, two values will be required to complete the following equation:

_________ ≤ µ ≤ __________

For this problem, what is the value that is below or less than µ?

23)  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 174 (µ = 174). The 30 individuals who take Atenolol have an average systolic blood pressure of 164, with a sample standard deviation of 26. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this problem!)

find out the 95% confidence interval.

As you know, two values will be required to complete the following equation:

_________ ≤ µ ≤ __________

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

24) The average time scheduled for a doctor’s visit is 17 minutes with a standard deviation of 20 minutes. A researcher uses a sampling distribution made up of samples of size 319. (Use these numbers for this problem only!)

According to the Central Limit Theorem, what is the standard error of the mean?

25) The average time scheduled for a doctor’s visit is 22 minutes with a standard deviation of 15 minutes. A researcher uses a sampling distribution made up of samples of size 318. (Use these numbers for this problem only!)

According to the Central Limit Theorem, what is the mean of the sampling distribution of means?

Statistics and Probability, Statistics

• Category:- Statistics and Probability
• Reference No.:- M91683

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