Question

Nutritionists are interested in comparing the absorption of calcium from calcium citrate malate (CCM)-fortified orange juice and CCM-fortified apple juice. They have a random sample of 48 women to use in this study. SELECT ALL THAT APPLY

Which of these study designs is a matched pairs design?                                                

	A.	The women are randomly assigned to one of two groups. Both groups were given a “standard” breakfast, but group one was given CCM apple juice and group two got CCM orange juice. Four hours later, the level of calcium in their blood is measured. The mean calcium levels of the two groups will be compared.
	B.	The women are randomly assigned to one of two groups. The study proceeded as in (A) but continued on the second day when each group had breakfast again but had the opposite juice -- group one came back for breakfast with CCM-orange juice and group two got CCM-apple juice this time. (This is a “cross-over” design.) Researchers noted the difference in calcium absorption for each woman after drinking orange juice and after drinking apple juice.
	C.	The women are randomly assigned to one of three groups. All three groups were given a “standard” breakfast, but group one was given CCM apple juice and group two got CCM orange juice. Group three was given their choice of non-fortified apple or orange juice. Four hours later, the level of calcium in their blood is measured. The mean calcium levels of the three groups will be compared.
	D.	The 48 women were offered given a standard breakfast and offered either CCM apple juice or CCM orange juice. Each woman was matched to her preferred juice. After 4 hours, the level of calcium in their blood was measured and the average calcium levels of women who chose orange juice was compared to the calcium levels of apple juice drinkers.

Scientists studying the behavior of spiders have 12 orb spiders in their lab. Many orb spiders spin a new web each day. Does the amount of ambient light affect the size of the web? For each spider, the scientists measured the horizontal diameter (in mm) of the web spun under bright light conditions one day, and under low light conditions on a different day.

Here is the data:

spider	1	2	3	4	5	6	7	8	9	10	11	12
bright light	190	260	280	250	160	210	290	120	210	160	240	270
low light	170	170	160	120	170	240	120	180	200	100	160	330

The scientists verified the normality of the data. They are testing the null hypothesis that the mean diameter is the same under both lighting conditions, versus there is a difference. The test statistic for testing H₀: μ = 0 versus H_a:  μ ≠ 0, where  μ = μ_diff which is equal to  μ_bright - μ_low, is _______________________ (give your answer to two decimal places)

Answer 1

(1)

Correct option:

B

EXPLANATION:
The 2 samples in this case are not independent. They are the same set of women:

Sample 1: Day 1: apple , Day 2: orange

Sample 2: Day1: orange, Day 2: apple

(2)

The values of d = bright - low are got as follows:

20, 90, 120, 130,- 10, - 30, 170, - 60, 10, 60, 80, 60

From the d values, the following statistics are calculated:

n = 12

= 640/12 = 53.3333

s_d = 69.3258

SE = s_d/

= 69.3258/ = 20.0126

Test statistic is:

t = /SE

= 53.3333/20.0126 = 2.66

So,

Test statistic is:

2.66

Take = 0.05

ndf = n- 1= 12 - 1= 11

From Table,critical values of t = 2.2010

Since the calculated value of t is greater than critical value of t, the difference is significant. Reject null hypothesis.

Conclusion:

Te data do not support the claim that the mean diameter is the same under both lighting conditions.

Answer to Question asked:

Test statistic is:

2.66