Question

Use the following information to answer the next 6 exercises. The Ice Chalet offers dozens of different beginning ice skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population. Use a 92% Confidence Interval for the true proportion of girls in the ages 8 - 12 beginning ice-skating classes at the Ice Chalet.

79. What is being counted?

81. Calculate the following:

a. x = _______ b. n = _______

a. lower limit b. upper limit c. error bound

83. In words, define the random variable P.

85. How much area is in both tails (combined)?

87. Calculate the following:

a. lower limit

b. upper limit

c. error bound

Answer 1

Answer)

Here we are counting number of girls, picked for skating

X = 64 and n = 64+16 = 80

P = 64/80 = 0.8

For 92% confidence interval

Critical value is 1.75

First divide 92 by 100 then subtract from 1

= 1-0.92

= 0.08

Then divide it by 2

= 0.04

So area in both the tails(combined) 0.08 an

And from z table 0.04 corresponds to 1.75

Standard error = √(p*(1-p)/n} = √(0.8*(1-0.8)/80)

= 0.04472135954

Margin of error = z*standard error

= 1.75*0.04472135954

MOE = 0.07826237921

Confidence interval is given by

Lower limit = P-MOE = 0.72173762078

Upper limit = P+MOE = 0.87826237921

Error = 0.07826237912