Question

I wanted to estimate the average height in feet of pine trees in my neighborhood. A random selection of 15 trees is as follows in feet: 48, 52, 92, 69, 75, 61, 85, 58, 79, 63, 73, 62, 57, 81, 68. What are the results of a 95% confidence interval for the mean height of pine trees in my neighborhood? Example: The following 95% Confidence Interval for a population mean is given, (3.6, 4.4). Find Lower Limit Find upper Limit Find margin of error Find sample mean, x ̅ What does the confidence interval say about the true population mean, μ?

Answer 1

Here, sample mean = 68.2
sample std.dev = 12.5823

t value at 95% confidence interval

df = n - 1 =15 - 1 =14

Margin of error= E = t *(s/sqrt(n))

= 2.1448 *(12.5823/sqrt(15))

= 6.9679

The 95% confidence interval for a population mean is xbar - E < mu < xbar + E 68.2 - 6.9679 , mu < 68.2+ 6.9679 61.2321 < mu < 75.1679 Upper limit = 75.1679 lower limit = 61.2321 We are 95% confident that the true population mean is between 61.2321 and 75.1679