Individual Exercises from E-Text

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Week 5 Individual Exercises From E-text

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5. State the main points of the Central Limit Theorum for a mean.

The Central Limit Theorum states that the sample mean x is centered at µand follows a normal distribution if n is large, regardless of the population shape.

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

The shape is a concern because if the shape is symmetrical, the mean will be near the center of the distribution. The mean is sensitive to extreme fluctuation values. If the distribution is not symmetrical, the mean will be away from the center and toward the extreme values. Since most statistics rely on normality, it is important to use the statistics that the underlying population is normally distributed ("Probability And Statistics Faq", N.D.).

8.46 A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477

(a) Construct a 90 percent confidence interval for the true mean weight.

Equation = z*∑/√n

1.6455 * 0.13199/(√10) = 0.06868136

(b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence?

= 3.3048

(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture. (Data are from a project by MBA student Henry Scussel.)

Factors which contribute to the variation of the weight of the Tootsie Rolls during manufacturing are temperature, batch consistency, and the tolerance of the machines producing them. The temperature that the Tootsie Rolls are made could cause weight variations. The amount of Tootsie Rolls made per batch could also play a part in determining the weight of the Tootsie Rolls. The tolerance of the machines are also a factor since we don't know how many Tootsie Rolls each machine can produce without being shut down for repair or to let the machine cool down.

Reference:

Probability and Statistics FAQ. (N.D.). Retrieved from http://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.330905.html