Question

In: Statistics and Probability

A study of 100 apple trees showed that the average number of apples per tree was...

A study of 100 apple trees showed that the average number of apples per tree was 1,000. The standard deviation of the population is 150. Which of the following is the 95% confidence interval for the mean number of apples for all trees? a.) (975.3, 1024.7) B.) (970.6, 1029.4) C.) (967.7, 1032.3) D.) (965.1, 1034.9)

Expert Solution

Solution :

Given that,

= 1000

= 150

n = 100

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (150 / $\sqrt$ 100)

= 29.4

At 95% confidence interval estimate of the population mean is,

- E < < + E

1000 - 29.4 < < 1000 + 29.4

970.6 < < 1029.4

(970.6 , 1029.4)

Option B) is correct

orchestra answered 2 years ago

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