Question

Studies have suggested that twins, in their early years, tend to have lower IQs and pick up language more slowly than nontwins. The slower intellectual growth might be caused by benign parental neglect. Suppose it is desired to estimate the mean attention time given to twins per week by their parents. A sample of 40 sets of 2 year old boys is taken, and after 1 week the attention time received was recorded. The data (in hours) calculated the mean at 26.1. The standard deviation was found to be 13.6. Use this information to construct a 90% confidence interval for the mean attention time given to all twin boys by their parents. Use at least 3 decimal places for your critical value, and give your answers to at least 2 decimal places.  

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 26.1  

Population standard deviation = = 13.6

Sample size = n = 40

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z0.05 = 1.645

Z/2 = 1.645  
Margin of error = E = Z/2 * ( /n)

= 1.645 * ( 13.6/  40 )

= 3.537

At 90 % confidence interval estimate of the population mean is,

- E < < + E

26.1 - 3.537 <   < 26.1+ 3.537

22.56 <   <29.64

(22.56 ,29.64 )