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In: Statistics and Probability

Are you an optimist? The General Social Survey asked 1373 men and 993 women in the...

  1. Are you an optimist? The General Social Survey asked 1373 men and 993 women in the United States whether they agreed that they were generally optimistic about the future. The results are presented in the flowing table.

Male

Female

Optimistic

1148

815

Pessimistic

225

178

  1. Compute the value of the chi square statistics.
  1. Can you conclude that the gender and the option on optimism are independent? using the α=0.05 level of significance
  1. Type Artificial hips: Artificial hip joints consist of a ball and socket. As the joint wears, the ball (head) becomes rough. Investigators performed wear tests on metal on metal artificial hip joints. Joints with several different diameters were tested. The following table presents measurements of head roughness (in nanometers).

Diameter

Head Roughness

16

0.83

2.25

0.4

2.78

3.23

28

2.72

2.48

3.8

36

6.49

5.32

4.59

  1. Construct an ANOVA table

Source

Degree of Freedom

Sum of Squares

Mean Squares

F Value

P Value

Treatment

Error

Total


  1. Can you conclude that mean roughness varies with diameter? Use the α=0.01 level of significance?

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