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.

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

Step-by-step 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)