A researcher is studying the calming effects of using profanity when in pain. To induce pain she asks participants to hold an ice cube. This is a common method of inducing pain in an ethical way for research purposes. She uses this method in a variety of studies. She then measures levels of cortisol (a steroid hormone known to increase under stressful circumstances). Consider the following three scenarios.. Your task is to determine what is the appropriate statistical procedure that should be used to analyze the data in each of the three scenarios. Scenario 1:

In one study, genetic contributions to this stress response were measured by using identical twins. She studied each twin separately and then compared the results of the two twins by finding the difference between their mean levels of cortisol. They were each asked to hold the ice cube for 3 minutes and were encouraged to curse if they needed pain relief. After testing many sets of twins she analyses their mean differences using a simple test on a single mean- the mean of the differences. A random sample of 20 sets of twins participated in this study. Scenario 2:

In another study, gender differences on pain tolerance were explored. A random sample of 20 males and 20 females participated in this study. They all were asked to hold the ice cube for 3 minutes and were encouraged to curse if they needed pain relief. After collecting the data, she computed the mean level of cortisol for the female group and for the male group and tested to see if there were any differences by gender. Scenario 3:

In a final study, the duration of the pain was manipulated to determine if this method works best in shorter or longer intervals (time). Sixty participants were randomly assigned to be in one of three groups. Group A was instructed to hold the ice cube for 1 minute and were encouraged to curse if they needed pain relief. Group B was instructed to hold the ice cube for 3 minutes and were encouraged to curse if they needed pain relief. Group C was instructed to hold the ice cube for 7 minutes and were encouraged to curse if they needed pain relief.

After collecting the data, she examined the relationship between time and cortisol. She uses a test to see if all the means are equal (null hypothesis) or if not all of the means are equal amongst the three groups.

Question 1 of 8

It has been suggested in previous research that women have a greater pain tolerance than men. Does the data in this study provide enough evidence to support this claim? In this study, gender differences on pain tolerance were explored. A random sample of 40 males and 40 females participated in this study. They all were asked to hold the ice cube for 3 minutes and were encouraged to curse if they needed pain relief. After collecting the data, she computed the mean level of cortisol for the female group and for the male group and tested to see if the data showed evidence that females have a greater pain tolerance than males. Let 11 and 22 be the mean cortisol level for each group respectively for the female and male groups. Which of the following are the appropriate hypotheses in this case?

H0:12=0Ha:12

H0:12=0Ha:12>0H0:1-2=0Ha:1-2>0

H0:120Ha:12=0H0:1-20Ha:1-2=0

H0:12

H0:12=0Ha:120H0:1-2=0Ha:1-20

H0:12>0Ha:12=0H0:1-2>0Ha:1-2=0

Question 2 of 8

80 adults, 40 women and 40 men were asked to hold an ice cube for 3 minutes and encouraged to curse if they were experiencing too much pain. The outcome (the response) is a measure of the cortisol at the conclusion of the painful experience (lower indicates higher pain tolerance) as measured by a medical expert who did not know the research question. Here are the summary statistics of cortisol data:

	Sample Size (n)	Mean (y)	SD (s)
Females	40	419	5.5
Males	40	422	3.5

Which of the following justifies why we can safely use the two-sample t-test in this case?

The two samples are independent AND both sample sizes are larger than 30.

The two samples are independent.

The two samples are both larger than 30.

The medical expert did not know which group each participant was assigned to and was blind to the hypotheses of the study

All of the above.

Question 3 of 8

When the two-sample t-test is carried out, the researchers find that the test statistic is t = 3.09 and P-value = 0.003P-value = 0.003 tells us that it would be quite unlikely to get results like that observed in our study (or more extreme) assuming that:

There is a difference between male and female pain tolerance.

There is no difference between male and female pain tolerance.

Males have a greater pain tolerance.

Females have a greater pain tolerance.

Question 4 of 8

The data analysis also found that the 95% confidence interval for 121-2 is (-4.93, -1.07 ).

Which of the following is the correct interpretation of this interval?

We are 95% confident that the mean cortisol score from the all of the female participants is between 4.93 to 1.07 points lower than the mean cortisol score from the all of the male participants.

There is 95% chance that any selected male participant will have a cortisol level between 4.93 to 1.07.

We are 95% confident that the cortisol score of any female participant is between 4.93 to 1.07 points lower than that of a male participant.

There is 95% chance that any selected female participant will have a cortisol level between 4.93 to 1.07.

Question 5 of 8

Recall that the P-value of the test for assessing whether females or males had a greater pain tolerance was P-value = 0.003. Which of the following is the appropriate conclusion? (Use significance level of 0.05).

Since Pvalue = 0.003

Since Pvalue = 0.003

Since Pvalue = 0.003

Since Pvalue = 0.003

Question 6 of 8

Consider a situation where we are testing:

H0:12=0Ha:120H0:1-2=0Ha:1-20

and the data analysis provides the following results:

	Sample Size (n)	Mean (y)	SD (s)
Group 1	40	7.3	1.5
Group 2	40	6.5	.5

• Test statistic: t=3.20t=3.20
• 95% confidence interval for 12:(.30,1.30)1-2:(.30,1.30)

Which of the following is correct regarding the P-value of the test?

The P-value must be larger than 0.05 since 0 falls outside of the 95% confidence interval for 121-2.

The P-value must be smaller than 0.05 since the test statistic t=3.20 falls outside of the 95% confidence interval for 121-2.

The P-value must be smaller than 0.05 since the test statistic t=3.20 falls outside of the 95% confidence interval for 121-2.

The P-value must be smaller than 0.05 since 0 falls outside of the 95% confidence interval for 121-2

Researchers measure depression levels before and after lottery winners receive their money. Past studies have shown that winning the lottery can increase depression. The depression scale that the researchers used is such that the higher the score the more depressed the individual is.

Do the data provide evidence that lottery winners became more depressed after receiving the money?

Let dd be the mean difference in depression score (Before money After money).

Question 7 of 8

Which of the following are the appropriate null and alternative hypotheses?

H0: d

H0: d =0Ha: d >0H0: d =0Ha: d >0

H0: d =0Ha: d 0H0: d =0Ha: d 0

H0: d =0Ha: d

Question 8 of 8

The researchers analyze the data and obtain the following output:

Which of the following is an appropriate conclusion based on the output?

The data do not provide sufficient evidence to reject the null hypothesis. Thus, the researcher can conclude that the depression scores of lottery winners were, on average, higher after they received their money.

The data do provide sufficient evidence to reject the null hypothesis. Thus, the researcher cannot conclude that the depression scores of lottery winners were, on average, higher after they received their money.

The data do provide sufficient evidence to reject the null hypothesis. Thus, the researcher can conclude that the depression scores of lottery winners were, on average, higher after they received their money.

Paired t test results P value and statistical significance: The two-tailed P value equals 0.0623 By conventional criteria, this difference is considered to be not quite statistically significant. Confidence interval: The mean of Group One minus Group Two equals -0.880 95% confidence interval of this difference: From -1.816 to 0.056 Intermediate values used in calculations: 2.1276 df 9 standard error of difference 0.414 Learn more: GraphPad's web site includes portions of the manual for GraphPad Prism that can help you learn statistics. First, review the meaning of P values and confidence intervals. Then learn how to interpret results from an unpaired or paired ttest. These links include GraphPad's popular analysis checklists Review your data: Group Group One Group Two Mean 8.470 9.350 SD SEM 0.766 0.973 0.242 0.308 10 10