Question

1. State the assumptions

2. State the appropriate confidence interval formula 3. find the confidence interval via calculator

4. write a full sentence for this interval

5. interpret the interval

Psychologists have found that twins, in their early years, tend to have lower intel- ligence and pick up languages more slowly than nontwins. The slower intellectual growth of twins may be caused by benign parental neglect. Suppose we want to investigate this phe- nomenon. A random sample of 50 sets of 2.5 year old twins boys was selected , and the total parental attention time given to each pair during 1 week is recorded. The data (in hours) are listed below.

20.7 14.0 16.7 20.7 22.5 48.2 12.1 7.7 2.9 22.2 23.5 20.3 6.4 34.0 1.3 44.5 39.6 23.8 35.6 20.0 10.9 43.1 7.1 14.3 46.0 21.9 23.4 17.5 29.4 9.6 44.1 36.4 13.8 0.8 24.3 1.1 9.3 19.3 3.4 14.6 15.7 32.5 46.6 19.1 10.6 36.9 6.7 27.9 5.4 14.0

Estimate the mean weekly attention time given to all 2.5 year old twin boys by their parents, using a 99% confidence interval. Interpret the interval.

Please write it out like the steps shown

Answer 1

1. We assume that the observations are independent and are drawn from a Normal population.

2. The 95% confidence Interval is given by

From Excel, we calculate the mean and the sd

	Time
	20.7
	14
	16.7
	20.7
	22.5
	48.2
	12.1
	7.7
	2.9
	22.2
	23.5
	20.3
	6.4
	34
	1.3
	44.5
	39.6
	23.8
	35.6
	20
	10.9
	43.1
	7.1
	14.3
	46
	21.9
	23.4
	17.5
	29.4
	9.6
	44.1
	36.4
	13.8
	0.8
	24.3
	1.1
	9.3
	19.3
	3.4
	14.6
	15.7
	32.5
	46.6
	19.1
	10.6
	36.9
	6.7
	27.9
	5.4
	14
Mean	20.848
SD	13.41383

The

The confidence interval is

  

  

Time
Confidence Level(95.0%)	3.812167

4. The 95% confidence interval for the population mean is between 17.0358 hours/week and 24.6602 hrs/week.

5. With 95% confidence, the true population mean lie between 17.0358 and 24.6602 hrs/week.