# Descriptive Statistics, Hypothesis Testing & Probability

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1. Draw a Frequency Distribution for the following data:

17, 1, 3, 4, 4, 16, 2, 2, 2, 7, 8, 7, 1, 2, 2, 5, 4, 3, 12, 9, 6, 3, 6, 10, 5, 2, 3, 11, 14, 2, & 2.

2. Describe briefly the shape of the Frequency Distribution in problem 1.

3. What is the median of the data in 1 above?

4. What is the mode in 1 above?

5. What is the mean of the data in 1 above?

6. The data in 1 above represent a sample drawn from a larger population. What is your best estimate of the population standard deviation?

7. In a certain city 10% of the residents are over 60 years old. What is the probability of finding no one over 60 in a sample of 10 residents?

8. Establish a 95% CI for m on the basis of the following sample statistics:

n = 100

-x = 10

s = 5

9. You are working with samples of the size 15 from the populations that are appx., normal distributed. What tables would you use to establish CI?

10. You suspect that two brands of soft drink differ in acidity. You measure the acidity of 10 randomly selected bottles of each brand with the following results:

Brand A Brand B

n = 10 n = 10

x = 6.50 x = 6.30

s = 0.05 s = 0.04

Outline an appropriate statistical test. What assumptions must you make, if any? Is the difference between the two brands significant at the 1% level?

11. The power of this test against the alternative µ = 5 is 0.80. Explain this statement:

The following data represent growth rates of plates before and after a chemical treatment. Outline an appropriate statistical test of the theory that the chemical treatment reduces growth rate. What assumptions must you make, if any? Are the results significant at the 5% level?

12. Complete the correlation coefficient between the before and after scores in problem 12.

13. Use a regression equation with the data of problem 12 to predict the after growth rate of a plant with a before growth rate of 3.

14. On the basis of sample data you wish to determine whether the variances of two populations differ. What statistical test will you use? Write the formula.

15. You wish to test the theory that men have higher self esteem than women. On the basis of a questionnaire you classify a group of men and woman into categories of high, medium, and low self-esteem. The results are as follows:

High Medium Low

Men 10 30 10

Women 25 15 10

17. Complete the analysis of Variance below. Are there significant differences between groups? (a = 0.01)

Sum of Squares df Variance estimate F

Total 580 29

Between Groups 175 2

Within groups 405 27

18. What assumptions are required for a two-way analysis of variance?

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis, descriptive statistics, binomial probability, confidence interval and regression analysis. The solution also provides assumption of independent t test, repeated measure t test and two way analysis of variance. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.