Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics grow procedure that utilized water containing the​ nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after germination. Those​ heights, measured in​ millimeters, were 55.7​, 59.5​, 60.2​, 63.7​, 65.9​, and 69.7   .Using​ technology, find the​ 95% confidence interval for the population mean μ. ​(Round to one decimal place as​ needed.)​(Round to one decimal place as​ needed.)

Question
Asked Nov 10, 2019

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics grow procedure that utilized water containing the​ nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after germination. Those​ heights, measured in​ millimeters, were 55.7​, 59.5​, 60.2​, 63.7​, 65.9​, and 69.7   .

Using​ technology, find the​ 95% confidence interval for the population mean μ. ​(Round to one decimal place as​ needed.)​(Round to one decimal place as​ needed.)

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Expert Answer

Step 1

The sample mean (point estimate for the population mean) is calculated as follows:

Sum of the observations
Мean 3
Number of observations
55.7 59.5 60.2 +63.7+65.9 +69.7
6
62.45
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Sum of the observations Мean 3 Number of observations 55.7 59.5 60.2 +63.7+65.9 +69.7 6 62.45

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Step 2

The sample standard deviation i...

6
Σ(-)
i1
п-1
|(55.7-62.45)++(69.7-62.45
=5.0071
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6 Σ(-) i1 п-1 |(55.7-62.45)++(69.7-62.45 =5.0071

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