In which of the following situations would it be appropriate to use a paired t-test to analyze the data?

Twins are screened for potential an environmental cancer risk factor and given an environmental risk factor score. Their outcomes are recorded and compared to their twin who had not been exposed to the same risk factor.

Participants are randomly assigned to a placebo or a control of a new cancer treatment to see if the medication is effective.

Patients being treated for cancer are asked whether they like their current treatment plan or not.

A researcher interviews 20 cancer patients and analyzes each interview for metaphorical themes and then summarizes the most common themes.

Researchers hypothesize that playing outside in dirt increases a child's immune system and helps them to get sick less often. In one study, researchers followed mothers for 6 months instructing them to keep their kids away from the dirt and use hand sanitizer at least once an hour (clean condition). In the following six months, the researchers changed their advice and encouraged moms to allow children to play in the dirt and avoid hand sanitizer (dirt condition). The total number of sicknesses in each time period was recorded. Then for each child, the difference between the two scores (dirt-clean) was calculated. The researchers hypothesized that the children would get fewer illnesses, when they were allowed to get dirty, as compared to when they had higher cleanliness standards.

Question 6

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If ₁ and ₂ represent the number of illnesses during the dirty and the clean condition, respectively, and let d be the mean of the differences in the number of correct answers (dirty-clean) of all children. Which are the appropriate null and alternative hypotheses?

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

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

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

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

Question 7

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The researchers analyzed the data and obtained the following output:

Summary statistics:

Sample	n	Mean	Variance	Std. Dev.	Std. Err.
Clean	50	35.3	41.438774	6.4372954	0.91037107
Dirt	50	38.7	41.030613	6.4055142	0.9058765

Hypothesis test results:

Difference	Sample Diff.	Std. Err.	DF	T-Stat	P-value
Dirt-Clean	-3.4	0.3736199	49	-9.100158	<0.0001

From the output we learn that:

The data provide sufficient evidence to reject H₀. Thus, the researchers conclude that children get, on average, fewer illnesses and when they are in dirty conditions as compared to clean conditions.

the data provide sufficient evidence to reject H₀. Thus, based on the data the researchers cannot conclude that children get, on average, fewer illnesses and when they are in dirty conditions as compared to clean conditions.

The data do not provide sufficient evidence to reject H₀. Thus, the researchers conclude that children get, on average, fewer illnesses and when they are in dirty conditions as compared to clean conditions.

The data do not provide sufficient evidence to reject H₀. Thus, based on the data the researchers cannot conclude that Thus, the researchers conclude that children get, on average, fewer illnesses and when they are in dirty conditions as compared to clean conditions.