Calculate the mean, median, sample variance, Applied Statistics

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Question:

The weights of 60 children born to mothers in a small rural hospital were recorded.

3.63

3.54

3.15

3.90

4.29

4.06

2.91

3.36

3.38

2.22

3.79

3.57

3.44

2.58

4.23

4.76

3.09

3.65

3.23

3.97

3.46

2.70

3.12

3.82

3.75

3.54

3.34

3.00

4.44

1.91

2.82

3.52

3.27

3.04

4.36

3.70

3.74

3.19

2.36

4.26

3.36

3.42

4.14

4.02

3.89

3.60

3.46

4.50

4.09

3.50

4.17

3.52

3.93

3.41

3.49

2.64

5.02

2.52

3.85

3.54

a) Calculate the mean, median, sample variance, and standard deviation of these results.

b) Calculate the 95% confidence intervals for this data set. Explain what these results are telling us in your own words. (Analyze - one sample t-test 95%)

c) What does a standard deviation tell you?

d) Suppose it is believed that the average weight for these children is 3 kg. At the 5% level of significance test whether the true weight for this group is 3 kg against the alternative hypothesis that the average weight is greater than 3 kg. You may assume that the data are normally distributed.

e) Draw a P-P plot for this data set. Would you consider this data to be normally distributed? Please justify your answer. (descriptive P-P plot)

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