Question

1) A machine used to fill beverage cans is supposed to put exactly 12 ounces of beverage in each can, but the actual amount varies randomly from can to can. The population standard deviation is σ = 0.05 ounce. A simple random sample of filled cans will have their volumes measured, and a 99% confidence interval for the mean fill volume will be constructed. How many cans must be sampled for the margin of error to be equal to 0.01 ounce?

2) Scientists want to estimate the mean weight of mice after they have been fed a special diet. From previous studies, it is known that the weight is normally distributed with standard deviation 3 grams. Find the sample size needed so that a 90% confidence interval will have a margin of error of 0.5 grams?

3) A cookie manufacturer wants to estimate the length of time that her boxes of cookies spend in the store before they are bought. She visits a sample of 45 supermarkets and determines the number of days since manufacture of the oldest box of cookies in the store. The sample mean is 54.8 days with a sample standard deviation of 11.3 days. Construct a 98% confidence interval for the mean number of days.

4) The General Social Survey asked 1972 adults how many years of education they had. The sample mean was 13.37 years with a standard deviation of 3.13 years. Construct a 90% confidence interval for the mean number of years of education.

Answer 1

Provided 0.01 margin of error is given, the population standard deviation σ=0.05 is provided, and the significance level is specified at 0.01, we can compute the minimum required sample size that will lead to a margin of error by using the following formula:

n=166

Ans2:.

n>9741.69

n=9742

Ans3:

=54.8

s=11.3

n=45

=1-c%=1-0.98=0.02

t/2,(n-1)=t0.01,44=2.41

ME=tc*s/sqrt(n)=2.41*11.3/sqrt(45)=4.07

98 % CI is (-ME,+ME)

(54.8-4.07,54.8+4.07)

(50.73,58.87)

Ans4:

=13.37

s=3.13

n=1972

=1-c%=1-0.90=0.1

tc=t/2,(n-1)=t0.05,1971=1.645

ME=tc*s/sqrt(n)=1.645*3.13/sqrt(1972)=0.418

98 % CI is (-ME,+ME)

(54.8-0.418,54.8+0.418)

(54.38,55.22)