Question

4. A sample of 36 bags of sugar produced by Domain sugar producers showed an average of 2 pounds and 2 ounces with a standard deviation of 7 ounces.

a. At 95% confidence, compute the margin of error and explain what it shows.

b. Determine a 95% confidence interval for the average weight of the population of bags of sugar produced by the company. Give the answer in ounces and at least two decimal places.

c. The bags of sugar produced are supposed to contain 2 pounds of sugar, but the company allows 1.5% higher or lower than the 2 pounds. Have they reached their desired goal? Explain why or why not by giving numerical facts.

Answer 1

Answer:

Given Data

1 ounce =0.0625 pounds

&

1 pound = 16 ounce

Here sample size n = 36

= 2 pounds and 2 ounces

= 2.125 pounds

= 34 ounces

S = sample standard deviation = 7ounces

Sample standard deviation is know , we shall use t - statistic , if population mean were given , we could use z - statistic.

a) Margin of error formula =

Here = 0.05 , S=7 , n= 36

L

So, the margin of error =

= 2.368459

= 2.37

= 0.0237%

The 95% confidence interval with a 0.0237% margin of error means  

It means the value of the true population mean will be within 0.0237% of the sample mean with 95% certainity.

b)

95% confidence interval for :

So , 95% confidence interval for is :

in ounces

c)

Here the Margin of error is 1.5% =0.015

here desired mean = 2 pounds

We know 95% confidence interval means :

Here = 0.125 > margin of error = 0.015 .

So , the difference between true mean and sample mean is greater than the margin of error .

So , they failed to reach their desired goal.