Answer to Question #341504 in Statistics and Probability for Adham

Question

The amount of material used in making a custom sail for a sailboat is normally distributed with a standard deviation of 64 square feet. For a random sample of 15 sails, the mean amount of material used is 912 square feet. Find a 90% confidence interval for the population mean amount of material used in a custom sail.

1. Point estimate value = 
2. Standard error (approximate to four decimal points) = 
3. Margin of error (approximate to four decimal points) = 
4. Tabulated value (approximate to four decimal points) = 
5. Upper limit (approximate to four decimal points) = 
6. Lower limit (approximate to four decimal points) = 

Answer 1

1. Point estimate value = 

$$\bar{x}=912/15=60.8$$

2. Standard error (approximate to four decimal points) = 

$$SE=\sigma/\sqrt{n}=64/\sqrt{15}=16.5247$$

3. Margin of error (approximate to four decimal points) = 

$$M=z_{\alpha/2}\times SE=1.6449\times\dfrac{64}{\sqrt{15}}=27.1815$$

4. Tabulated value (approximate to four decimal points) = 

$$z_{\alpha/2}=1.6449$$

5. Upper limit (approximate to four decimal points) = 

$$60.8+16.5247=77.3247$$

6. Lower limit (approximate to four decimal points) = 

$$60.8-16.5247=44.2753$$