Question

Rosetta is an occupational therapist working in a Head Start program. The program serves 4-year-old children at risk of not passing the kindergarten screening test at age 5. One of the tasks on the kindergarten screening test is fine motor control at a level that makes cutting, coloring, and writing (name, alphabet) possible. To assist the children in developing fine motor control, Rosetta assists each child in fine motor exercises for a period of 1/2 hr a day over a period of 6 months. She wonders if the children’s fine motor skills significantly improved as a result of her instruction. Here are each child’s scores on a 10-point fine motor scale before and after instruction. Higher scores indicate more fine motor control:

Subject
Fine Motor Score Before Instruction Fine Motor Score After Instruction
Quincy 3 5
Rolf 2 6
Stu   4 6
Tevya 5 6
Ulysses 3 3
Victor 4 7
Willy 3 4
Xerxes 2 4
Yekio 3 7
Zack 5 5

(a) Calculate t and compare it to a one-tailed critical t at the .05 level. Did Rosetta’s instruction result in significantly better fine motor control?

(b) The design of this study is not ideal because it is possible that the children’s motor ability would have improved over the 6-month period even without instruction. How could the design of this study be changed in order to eliminate this problem?

Answer 1

(a) Calculate t and compare it to a one-tailed critical t at the .05 level. Did Rosetta’s instruction result in significantly better fine motor control?

The hypothesis being tested is:

H0: µd = 0

Ha: µd < 0

Before	After
3	5
2	6
4	6
5	6
3	3
4	7
3	4
2	4
3	7
5	5
3.400	mean Before
5.300	mean After
-1.900	mean difference (Before - After)
1.449	std. dev.
0.458	std. error
10	n
9	df
-4.146	t
.0012	p-value (one-tailed, lower)

The p-value is 0.0012.

Since the p-value (0.0012) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that Rosetta’s instruction result in significantly better fine motor control.

(b) The design of this study is not ideal because it is possible that the children’s motor ability would have improved over the 6-month period even without instruction. How could the design of this study be changed in order to eliminate this problem?

Consider the first group of childern with motor ability after the instruction and consider another group of children with motor ability after the instruction. This design would tell if there is a difference in Rosetta’s instruction result in significantly better fine motor control.

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