Problem: Define the sampling distribution for the difference between two independent sample means. Draw and completely label the sampling distribution for the difference between two independent sample means.

Problem: What assumptions are required for ANOVA?

1. Draw and completely label the F distribution.
2. When analyzing a particular data set using either independent sample t test or ANOVA, the relationship of the "t calculated" to the "F calculated" is (circle the correct one):
   1. F ² = t
   2. F= t ²
   3. F = 1/t
      

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3. (TRUE or FALSE)______ A "statistically significant F" in ANOVA indicates that you have identified which treatments are different from the others.
4. Draw and completely label the \[{{\chi }^{2}}\] distribution

1. (25 points)

An experiment compared the weight of poplar trees (seedlings) grown for a year under two different fertilization strategies (Control and Fertilized). Twenty (n ₁ =20, n ₂ =20) poplar seedlings were randomly assigned to these two levels of fertilization strategies. A partial statistical output is s shown below.

Statistics

Variable Treatment N Mean

weight Control 20 0.6465 \[({{\bar{x}}_{c}})\]

weight Fertilized 20 1.3365 \[({{\bar{x}}_{f}})\]

weight Diff (1-2) _______ _______

Variable Treatment Variances

weight Control 0.3224 \[(S_{c}^{2})\]

weight Fertilized 0.5190 \[(S_{f}^{2})\]

Pooled Variance ________

Pooled Standard Deviation_ ____

Standard Er ror for differences of means __ ___

t Value(calculated)_ ______

t critical (from table)_ _____

1. Calculate a 95% confidence interval for the difference between population means. Complete all underlined blank spaces in the output above and give an inference of the confidence interval.
   NAME:____________________________
2. Based on the completed output, test the hypothesis (Ho) of no difference in weight between the t wo fertilization strategies against the alternative (Ha) that fertilization strategies are different . ONLY include the following steps of hypothesis testing:

1. Formulate the hypotheses (Ho and Ha):

6) Your DECISION:

7) COMPLETE INFERENCE:

1. Without doing any test, d o you think the assumption of equal variances is met? Explain (briefly).
2. How might you have used the confidence interval to draw the same conclusion as with the results of the test of significance included in the SAS output. Explain using the confidence interval calculated in a)

1. (15 points)

A manufacturer wishes to compare the wearing qualities of two different types of automobile tires, A and B. For the comparison, a tire of type A and one of type B are randomly assigned and mounted on the rear wheels of each of five automobiles. The automobiles are then operated for a specified number of miles and the amount of wear is recorded for each tire.

1. Calculate a 95% confidence interval for the difference between the population means. Give an interpretation of the confidence interval.
2. Using the confidence interval calculated in a) as a tool for hypothesis testing, make an inference about the hypothesis that both types of types of tires have the same wearing qualities.

1. (15 points)

A manufacturer of hard safety hats for construction workers is concerned about the variation of the forces helmets transmit to wearers when subjected to an external force A random sample of forty one (n=41) helmets was tested and the Sample Variance (S ² ) was found to be 2350 pounds ² .

1. Using the sample variance, construct a 95% confidence interval to estimate the Population Standard Deviation for the force transmitted by helmets.
2. Does your CI provides enough evidence to indicate that the population standard deviation is different than 35? Explain briefly.

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Solution: The downloadable solution consists of 11 pages, 942 words and 3 charts.
Deliverable: Word Document