Chapter 8 Exercises

Cindy Blando

Chapter 8 Exercises

5. State the main points of the Central Limit Theorem.

The mean of a sampling distribution is equal to the mean of the population from where the samples came from.

The variance of the sample distribution is equal to the variance of the population divided by two.

If the original population is distributed equally then the sample distribution will also be equal. If not then the sample distribution will increase as the sample increases.

6. Why is the population shape of concern when estimating a mean? What does the sample size have to do with it?

If you are able to apply the central limit theorem (the sample population is a normal distribution) then you can draw conclusions from the samples based on the shapes such as bell shaped samples or not. The size of the sample can increase or decrease causing better estimations of the population’s mean.

8.42

The standard error is 1.96(s/srt(n))= 1.96 times .0131989/sqrt(10)= 1.96 times .41739 which equals.081808

Part b) if the error is .03 with 90% confidence interval

Equation is n=z /E squared to 2

N=1.645x.131989/.03 squared= 52.38 rounded up to 53

c. There are many reasons for variation in the weight of the Tootsie Rolls. It could have happened in production. Too many ingredients in one versus the other roll or the machinery could be off causing one roll to be slightly bigger than the other one.

8.62 – not able to work out the solution