Question 7 6 points The owner of the House of Greens Greenho

Question 7 [6 points]

The owner of the House of Greens Greenhouse wants to estimate the mean height that her seedlings grow. A sample of 26 plants were chosen and their growth was recorded over a period of a month. It was found that the sample mean was 24.00 cm and the sample standard deviation was 4.64 cm. Given this information, develop a 99.0% confidence interval estimate for the population mean (assuming the best point estimate for the population mean is the sample mean and that the population standard deviation is not known).  
For full marks your answer should be accurate to at least three decimal places.

Confidence interval: ( 0, 0 )

Question 7 [6 points] The owner of the House of Greens Greenhouse wants to estimate the mean height that her seedlings grow. A sample of 26 plants were chosen and their growth was recorded over a period of a month. It was found that the sample mean was 24.00 cm and the sample standard deviation was 4.64 cm. Given this information, develop a 99.0% confidence interval estimate for the population mean (assuming the best point estimate for the population mean is the sample mean and that the population standard deviation is not known). For full marks your answer should be accurate to at least three decimal places. Confidence interval: ( 0, 0 )

Solution

The degree of freedom =n-1=26-1=25

Given a=1-0.99= 0.01, t(0.005, df=25) =2.79 (from student t table)

So the lower bound is

xbar - t*s/vn =24 - 2.79*4.64/sqrt(26) =21.46116

So the upper bound is

xbar + t*s/vn =24 + 2.79*4.64/sqrt(26) =26.53884