# What is the probability that this adult likes chocolate ice cream?

Statistics Quiz

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1.An economist says that the probability is 0.47 that a randomly selected adult is in favor of keeping the Social Security system as it is, 0.32 that this adult is in favor of totally abolishing the Social Security system, and 0.21 that this adult does not have any opinion or is in favor of other options. Were these probabilities obtained using the classical approach, relative frequency approach, or the subjective probability approach?

A. Classical probability approach.

B. Relative frequency approach.

C. Subjective probability approach.

2. In a sample of 300 adults, 111 like chocolate ice cream and 96 like vanilla ice cream. One adult is randomly selected from these adults. Round your answer to 2 decimal places.

a. What is the probability that this adult likes chocolate ice cream?

Probability =

b. What is the probability that this adult likes vanilla ice cream?

Probability =

c. Do these two probabilities add to 1.0?

3. In a sample of 500 families, 50 have a yearly income of less than $50,000, 210 have a yearly income of $ 50,000 to $ 100,000, and the remaining families have a yearly income of more than $ 100,000.

Write the frequency distribution table for this problem. Calculate the relative frequencies for all classes.

Income Frequency Relative

Less than 50k

50k to 100K

More than 100K

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Order Paper NowSuppose one family is randomly selected from these 500 families. Find the probability that this family has a yearly income of less than $ 50,000.

P(income is less than $ 50,000)=

b. Suppose one family is randomly selected from these 500 families. Find the probability that this family has a yearly income of more than $ 100,000.

P(income is more than $ 100,000)=

4. Classify the following random variable as discrete or continuous.

The time left on a parking meter.

5. Classify the following random variable as discrete or continuous.

The number of bats broken by a major league baseball team in a season.

6. The following table lists certain values of x and their probabilities. Verify whether or not it represents a valid probability distribution.

X p(x)

0 0.36

1 0.30

2 0.19

3 0.12

The table (does or does not represent) a valid probability distribution?

7. The following table gives the probability distribution of a discrete random variable x.

X 0 1 2 3 4 5 6

P(x) 0.12 0.19 0.29 0.15 0.12 0.07 0.06

Find P(x≥4).

P(x≥4)=

8. The following table gives the probability distribution of a discrete random variable x.

X 0 1 2 3 4 5 6

P(x) 0.11 0.20 0.28 0.15 0.12 0.07 0.07

Find P(x≥2).

P(x≥2)=

9. . The following table gives the probability distribution of a discrete random variable x.

X 0 1 2 3 4 5 6

P(x) 0.13 0.19 0.30 0.15 0.12 0.09 0.02

Find P(1≤x≤4).

P(1≤x≤4)=

10. Find the mean and standard deviation for the following probability distribution.

X P(x)

6 0.38

7 0.23

8 0.22

9 0.17

Enter the exact answer for the mean and round the standard deviation to three decimal places.

Mean =

Standard deviation =

11. Which of the following are binomial experiments?

a. Rolling a die many times and observing the number of spots. Binomial or Non

b. Rolling a die many times and observing whether the number obtained is even or odd. Binomial or Non

c. Selecting a few voters from a very large population of voters and observing whether or not each of them favors a certain proposition in an election when 54% of all voters are known to be in favor of this proposition. Binomial or Non

12. According to a survey, 75% of households said that they have never purchased organic fruits or vegetables. Suppose that this result is true for the current population of households.

a. Let x be a binomial random variable that denotes the number of households in a random sample of 10 who have never purchased organic fruits or vegetables. What are the possible values that x can assume?

Integers ( ) to ( ).

b. Find to 3 decimal places the probability that exactly 6 households in a random sample of 10 will say that they have never purchased organic fruits or vegetables. Use the binomial probability distribution formula.

Probability =

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SPSS : Introduction to Probability and Statistics

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Answer each question completely, showing all your work. Copy and Paste the SPSS output into the word document for the calculations portion of the problems. (Please remember to answer the questions you must interpret the SPSS output).

A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest).

Participant Hours of Exercise Life Satisfaction

1 3 1

2 14 2

3 14 4

4 14 4

5 3 10

6 5 5

7 10 3

8 11 4

9 8 8

10 7 4

11 6 9

12 11 5

13 6 4

14 11 10

15 8 4

16 15 7

17 8 4

18 8 5

19 10 4

20 5 4

Find the mean hours of exercise per week by the participants.

Find the variance of the hours of exercise per week by the participants.

Determine if there is a linear relationship between the hours of exercise per week and the life satisfaction by using the correlation coefficient.

Describe the amount of variation in the life satisfaction ranking that is due to the relationship between the hours of exercise per week and the life satisfaction.

Develop a model of the linear relationship using the regression line formula.

Insomnia has become an epidemic in the United States. Much research has been done in the development of new pharmaceuticals to aide those who suffer from insomnia. Alternatives to the pharmaceuticals are being sought by sufferers. A new relaxation technique has been tested to see if it is effective in treating the disorder. Sixty insomnia sufferers between the ages of 18 to 40 with no underlying health conditions volunteered to participate in a clinical trial. They were randomly assigned to either receive the relaxation treatment or a proven pharmaceutical treatment. Thirty were assigned to each group. The amount of time it took each of them to fall asleep was measured and recorded. The data is shown below. Use the appropriate t-test to determine if the relaxation treatment is more effective than the pharmaceutical treatment at a level of significance of 0.05.

Relaxation Pharmaceutical

98 20

117 35

51 130

28 83

65 157

107 138

88 49

90 142

105 157

73 39

44 46

53 194

20 94

50 95

92 161

112 154

71 75

96 57

86 34

92 118

75 41

41 145

102 148

24 117

96 177

108 119

102 186

35 22

46 61

74 75

A researcher is interested to learn if there is a relationship between the level of interaction a women in her 20s has with her mother and her life satisfaction ranking. Below is a list of women who fit into each of four level of interaction. Conduct a One-Way ANOVA on the data to determine if a relationship exists.

No Interaction Low Interaction Moderate Interaction High Interaction

2 3 3 9

4 3 10 10

4 5 2 8

4 1 1 5

7 2 2 8

8 2 3 4

1 7 10 9

1 8 8 4

8 6 4 1

4 5 3 8

Is there a relationship between handedness and gender? A researcher collected the following data in hopes of discovering if handedness and gender are independent (Ambidextrous individuals were excluded from the study). Use the Chi-Square test for independence to explore this at a level of significance of 0.05.

Left-Handed Right-Handed

Men 13 22

Women 27 18

A researcher is interested in studying the effect that the amount of fat in the diet and amount of exercise has on the mental acuity of middle-aged women. The researcher used three different treatment levels for the diet and two levels for the exercise. The results of the acuity test for the subjects in the different treatment levels are shown below.

Diet

Exercise <30% fat 30% – 60% fat >60% fat

<60 minutes 4 3 2

4 1 2

2 2 2

4 2 2

3 3 1

60 minutes 6 8 5

or more 5 8 7

4 7 5

4 8 5

5 6 6

Perform a two-way analysis of variance and explain the results. (Show all work to receive full credit)

Find the effect size for each factor and the interaction and explain the results. (Show all work to receive full credit)

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