Question

In a random sample of 7 residents of the state of California, the mean waste recycled per person per day was 1.5 pounds with a standard deviation of 0.58 pounds. Determine the 99% confidence interval for the mean waste recycled per person per day for the population of California. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

CI(99%) = ( 0.93 , 2.07)

Therefore at 99% confidence interval (a,b) = ( 0.93 , 2.07)

Critical value z(at 99% confidence) = z(0.005) = 2.58

Explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean gain x = 1.5

Standard deviation r = 0.58

Number of samples n = 7

Confidence interval = 99%

Critical value z(at 99% confidence) = z((1-0.99)/2)

z(0.005) = 2.58

Substituting the values we have;

1.5+/-2.58(0.58/√7)

1.5+/-2.58(0.2192)

1.5+/-0.565536

1.5+/-0.57

= ( 0.93 , 2.07)

Therefore at 99% confidence interval (a,b) = ( 0.93 , 2.07)