Answer to Question #182133 in Statistics and Probability for Apple Assignexpt Guirhem

Question

Solve the given problem. Find the following and show your complete solution.

a. Critical Value

b. Margin of Error

c. Confidence Interval

GIVEN:

The average test scores in a Science class is normally distributed with a standard deviation of 8. 200 scores with a sample mean of 170 were selected at random. Estimate the population mean with:

a. 85% confidence

b. 90% confidence

c. 95% confidence

Answer 1

a)85% confidence

i)The critical value is 1.44

ii)the margin of error= critical value*standard deviation

=1.44*8.200

=11.808

iii) confidence interval=mean±margin of error

=170±11.808

(158.192,181.808)

b)90% confidence

i) the critical value is 1.645

ii)the margin of error= critical value*standard deviation

=1.645*8.200

=13.489

iii) confidence interval=mean±margin of error

=170±13.489

(156.511,183.489)

c)95% confidence

i)The critical value is 1.96

ii)the margin of error= critical value*standard deviation

=1.96*8.200

=16.072

iii) confidence interval=mean±margin of error

=170±16.072

(153.928,186.072)