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In: Statistics and Probability

A study of 35 apple trees showed that the average number of apples per tree was...

A study of 35 apple trees showed that the average number of apples per tree was 725. The standard deviation of the population is 100. Which of the following is the 99% confidence interval for the mean number of apples per tree for all trees?

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Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 725

Population standard deviation =    = 100
Sample size = n =35

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

Margin of error = E = Z/2* ( /n)

=2.576 * (100 / 35)

= 43.5423

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

- E < < + E

725-43.5423 < < 725+43.5423

681.4577< < 768.5423

( 681.4577, 768.5423)

orchestra answered 2 years ago
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