In a study of the length of time it takes to earn an associate’s degree, a...

In a study of the length of time it takes to earn an associate’s degree, a random sample of 41 students had a mean of 2.8 years. Assume that the population standard deviation is 0.9 years. You wish to construct a 99% confidence interval for the mean time it takes to earn an associate's degree. Use this information to answer the next 5 questions. (Be sure to use the correct distribution.)

What is the confidence interval? Round to 2 decimal places.

If applicable, what are the degrees of freedom? (Type NA if not applicable.)

What is the critical value?

What is the point estimate?

What is the margin of error? Round to 2 decimal places.

Solutions

Expert Solution

Solution :

Given that,

1) Point estimate = sample mean = = 2.8 years

Population standard deviation = = 0.9 years

Sample size = n = 41

2) degrees of freedom = NA

3) At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_0.005 = 2.576

4) Margin of error = E = Z/2 * ( / $\sqrt$ n)

E = 2.576 * ( 0.9 / $\sqrt$ 41 )

E = 0.36

5) At 99% confidence interval estimate of the population mean is,

± E

2.8 ± 0.36

( 2.44, 3.16 )

orchestra answered 1 year ago

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