Ohio University Module 7 Sample T Summary Hypothesis Test Worksheet Instructions

If the question requires computation, do the calculations and then give or select the correct values using the following rule:

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Ohio University Module 7 Sample T Summary Hypothesis Test Worksheet Instructions
If the question requires computation, do the calculations and then give o

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Keep at least 4 decimal places at intermediate steps of a calculation, and round your final answer to 2 decimal places, unless otherwise noted.

For example:

16.6667 would become 16.67 after rounding

(In the course notes for Module 7, probabilities such .678934 are instead rounded to four decimal places, so the correct way to report the aforementioned probability is .6789)

Multiple Attempts

Force Completion

Question 1

The following 5 questions (Q1 to Q5) are based on the following example:

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 sample mean of 39.5 and a sample standard deviation of 6.6.

The appropriate statistical procedure for this example would be a

z-test

t-test

Question 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 sample mean of 39.5 and a sample standard deviation of 6.6.

Is this a one-tailed or a two-tailed test?

one-tailed

two-tailed

Question 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 sample mean of 39.5 and a sample standard deviation of 6.6.

The most appropriate null hypothesis (in words) would be

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

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

Being bullied does significantly increase empathy when compared to the population of individuals in the general population who have not been bullied.

Being bullied does not significantly increase empathy when compared to the population of individuals in the general population who have not been bullied.

Question 4

The most appropriate null hypothesis (in symbols) would be

?empathy = 39.5

?empathy = 30.6

?empathy > 39.5

?empathy > 30.6

Question 5

Test at the .05 level of significance.

Set up the criteria for making a decision. That is, find the critical value using an

alpha = .05. (Make sure you are sign specific: + ; – ; or ± ) (Use your tables)

-1.645

±1.645

±2.756

2.064

±2.064

Question 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 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? (numeric value only)

Question 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 59.39. Random sampling of 51 scores obtained from individuals who were bullied yielded a mean of 54.72 and a standard deviation of 8.69. (Use these numbers only for this question!)

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

Question 8

Test at the .05 level of significance.

Suppose that the value of your calculated (obtained) test statistic is 6.74. What is your decision?

reject the null hypothesis

fail to reject the null hypothesis

reject the alternative hypothesis

Question 9

Test at the .05 level of significance.

The best conclusion for this example (based on your answer to Q8) 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.

Question 10

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

Type I statistical error

Type II statistical error

Question 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 61.23. Random sampling of 76 scores obtained from individuals who were bullied yielded a mean of 44.07 and a standard deviation of 22.87. (Use these numbers only for this question!)

Suppose you want to calculate the 99% confidence interval.

The mean you will use for this calculation is:

Question 12

Suppose you want to calculate 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

Question 13

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 65.49. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 61 and a standard deviation of 20.11. (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 below or less than µ?

Question 14

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 57.14. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 69.38 and a standard deviation of 8.91. (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?

Question 15

If ? = 0.14, and ? = 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 reject the null, and H0 is really true (i.e., a Type I error)

Question 16

If ? = 0.06, and ? = 0.09, 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)

Question 17

If ? = 0.15, and ? = 0.16, 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)

Question 18

If ? = 0.07, and ? = 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 fail to reject the null, and H0 is really false (i.e., a Type II error)

Question 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 sample of 30 individuals who take Atenolol have an average (mean) 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:

t-test

z-test

chi-square goodness of fit

chi-square test for independence

Question 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 sample of 30 individuals who take Atenolol have an average (mean) 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?

one-tailed

two-tailed

Question 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 sample of 30 individuals who take Atenolol have an average (mean) 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 most appropriate alternative hypothesis (in words) 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 increase in systolic blood pressure when comparing people who take Atenolol to the general population of people who do not take Atenolol.

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

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

Question 22

The most appropriate alternative hypothesis (in symbols) would be:

µBloodPressure = 165

µBloodPressure = 147

µBloodPressure < 165 µBloodPressure< 147 Question 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 165 (µ = 165). The sample of 30 individuals who take Atenolol have an average (mean) 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 Question 24 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 114 individuals who take Atenolol have an average systolic blood pressure of 147, with a sample standard deviation of 11.89. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this question!) What is the numeric value of your standard error? Question 25 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 162 (µ = 162). The 167 individuals who take Atenolol have an average systolic blood pressure of 121, 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 question!) What is the z-value or t-value you obtained (your test statistic)? (numeric value only, including negative sign if required) Question 26 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 sample of 30 individuals who take Atenolol have an average (mean) 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. Suppose that the value of your calculated (obtained) test statistic is -16.51. What is your decision? Reject the null hypothesis Fail to reject the null hypothesis Question 27 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 sample of 30 individuals who take Atenolol have an average (mean) 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 example (based on your answer to Q26) 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 higher systolic blood pressure when compared to the general population of people who do not take Atenolol. Question 28 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 sample of 30 individuals who take Atenolol have an average (mean) 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 (Q26), and your conclusion in Q27, as a researcher, you would be more concerned with a: Type I statistical error Type II statistical error Question 29 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 179, 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 question only!) Calculate the 95% confidence interval The mean you will use for this calculation is: Question 30 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 sample of 30 individuals who take Atenolol have an average (mean) 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? Calculate 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 Question 31 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 150 (µ = 150). The 30 individuals who take Atenolol have an average systolic blood pressure of 167, with a sample standard deviation of 14. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this question!) Calculate the 95% 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? Question 32 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 156 (µ = 156). The 30 individuals who take Atenolol have an average systolic blood pressure of 159, with a sample standard deviation of 23. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this question!) Calculate the 95% 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 above or greater than µ? 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 156 (µ = 156). The 30 individuals who take Atenolol have an average systolic blood pressure of 159, with a sample standard deviation of 23. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this question!) Calculate the 95% 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 above or greater than µ? Question 33 The average time scheduled for a doctors visit is 17 minutes with a standard deviation of 14 minutes. A researcher uses a sampling distribution made up of samples of size 92. (Use these numbers for this question only!) According to the Central Limit Theorem, what is the standard error of the mean? Question 34 The average time scheduled for a doctors visit is 9 minutes with a standard deviation of 8 minutes. A researcher uses a sampling distribution made up of samples of size 152. (Use these numbers for this question only!) According to the Central Limit Theorem, what is the mean of the sampling distribution of means? Question 35 Which of the following is most likely to increase the calculated value of a t-test? Increase the number of subjects Decrease the number of subjects Repeat with a convenience sample Repeat with the same sample Repeat with a stratified random sample Question 36 As you increase the true distance between the null and alternative hypotheses, the likelihood of rejecting the null hypothesis Increases Decreases Remains the same Question 37 Keeping everything else the same, if you were to change your alpha level from .01 to .05, the likelihood of rejecting the null hypothesis Increases Decreases Remains the same Question 38 In a research setting, it is more common to use t-tests than z-tests because Typically the population mean is unknown. Typically the population standard deviation is unknown. They are more accurate since sample size is taken into account when determining critical values. Typically the sample mean is unknown. "t" comes before "z" in the alphabet Question 39 What is the basic question that underlies hypothesis testing? Is the sample representative of the population? Could the relationship observed in the sample have occurred by chance? What is the standard score? Should we reject the null hypothesis?

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