Question

1. ): Infants who cry easily may be more easily stimulated than others. This may be a sign of higher IQ. Child development researchers explored the relationship between the crying of infants four to ten days old and their later IQ test scores. A snap of a rubber band on the sole of the foot caused the infants to cry. The researchers recorded the crying and measured its intensity by the number of peaks in the most active 20 seconds. They later measured the children’s IQ at age three years using the Stanford-Binet IQ test. Table contains data on 38 infants. We need to construct a linear regression equation.

	INFANTS' CRYING (NUMBER OF PEAKS)			INFANTS' CRYING (NUMBER OF PEAKS)
	AND IQ SCORES			AND IQ SCORES
CRYING	IQ		CRYING	IQ
10	87		13	162
12	97		17	94
9	103		19	103
16	106		13	104
18	109		18	109
15	114		18	112
12	119		16	118
20	132		19	120
16	136		22	135
33	159		30	155
20	90		12	94
16	100		12	103
23	103		14	106
27	108		10	109
15	112		23	113
21	114		9	119
12	120		16	124
15	133		31	135
17	141		22	157

1. Give a 95% confidence interval for β . Test the hypotheses in (c) using the confidence interval. Do you get the same answer as (c) and (d)? Interpret the test findings if the answer is different than (c) and (d).

2. Write down the null and alternative hypotheses to test if the slope β is significantly greater than 1. Test the hypotheses using an appropriate confidence interval. Interpret the test result.

3. Write down the null and alternative hypotheses to test if the slope β is significantly lesser than 3. Test the hypotheses using an appropriate confidence interval. Interpret the test result.

4. Write down the null and alternative hypotheses to test if the slope β is significantly greater than 3. Test the hypotheses using an appropriate confidence interval. Interpret the test results.

Answer 1

### Answers:

a]95% confidence interval for slope b is (0.7996 , 2.5507 )

we will get same answer

b] Null & alternative hypothesis are

H0: β <=1

H1: β >1

Since the lower limit of 95% confidence interval is smaller than 1, we can not conclude that the slope β is greater than 1

c] H0: β >=3

H1: β<3

Since the upper limit of 95% confidence interval is greater than 3, we can conclude that the slope β is less than 3

d]

H0: β <=3

H1: β>3

Since the lower limit of 95% confidence interval is smaller than 3, we can not conclude that the slope β is greater than 3