A guy wants to estimate the mean time it takes his plants to mature. He takes a

Question

A guy wants to estimate the mean time it takes his plants to mature. He takes a sample of 12 stalks and records the number of days between planting and maturing. The data is following: 62 68 59 85 73 78 61 82 75 79 80 71

What would be the point estimate for the mean number of days that it takes his corn to mature?


Compute the 95% confidence interval of the number of days the corn takes to mature?


What is the margin of error in the confidence interval?



Interpret the confidence interval from above.

Explanation / Answer

Given n=12, s= 8.68 (based on the data)
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What would be the point estimate for the mean number of days that it takes his corn to mature?

xbar=(62+ 68+ 59+ 85+ 73+ 78+ 61+ 82+ 75+ 79+ 80+ 71)/12 =72.75

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Compute the 95% confidence interval of the number of days the corn takes to mature?

Given a=0.05, t(0.025, df=n-1=11)=2.2 (check student t table)

So 95% CI is
xbar ± t*s/n

--> 72.75 ± 2.2*8.68/sqrt(12)

--> (67.24, 78.26)

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What is the margin of error in the confidence interval?

margin of error = t*s/n = 2.2*8.68/sqrt(12) = 5.51254

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Interpret the confidence interval from above.

We have 95% confidence that the number of days the corn takes to mature in (67.24, 78.26).

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