Question

The owner of the House of Greens Greenhouse wants to estimate the mean height that her seedlings grow. A sample of 11 plants were chosen and their growth was recorded over a period of a month. It was found that the sample mean was 10.00 cm and the sample standard deviation was 4.98 cm. Given this information, develop a 95.0% confidence interval estimate for the population mean (assuming the best point estimate for the population mean is the sample mean).

For full marks your answer should be accurate to at least three decimal places.

Confidence Interval:

Answer 1

Solution :

Given that,

= 10

s = 4.98

n = 11

Degrees of freedom = df = n - 1 = 11 - 1 = 10

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,10 = 2.228

Margin of error = E = t_/2,df * (s /n)

= 2.228 * (4.98 / 11)

= 3.345

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

- E < < + E

10 - 3.345 < < 10 + 3.345

6.655 < < 13.345

(6.655, 13.345)