Statistics Assignment -
Use the following information to answer questions 1-6.
The international Symposium on Human Psyche published a report stating that 75% of all adults believe that it is important to be involved in their communities. You and your colleagues conducted a small-scale survey, polling 1025 randomly selected adults, and found that 91% believe that it is important to be involved in their community. Assume that the data has a binomial distribution and meets the criteria to be approximated by a normal distribution. Use a significance level of α = 0.05 to test the claim that the population proportion is not 75%.
Q1. What would be the recorded number of adults from your sample that responded that they believe it is important to be involved in their communities?
A) 933
B) 1025
C) 91
D) None of These
Q2. State the hypotheses:
A) H0 : p = 0.75, H1 : p ≠ .75)
B) H0 : μ = 0.75, H1 : ≠μ ≠ .75
C) H0 : p = 0.75, H1 : p < .75
D) None of These
Q3. What "tail type" is this test?
A) Upper Tail
B) Two-Tailed
C) Lower Tail
D) None of These
Q4. You conduct a critical value test. What is your critical value?
A) z = 1.96
B) z = 11.848
C) z = 0.95
D) None of These
Q5. What is your test statistic?
A) z = 0.910
B) z = 1 1.848
C) z = 1
D) None of These
Q6. Draw a picture of the normal curve, identifying the location and numerical value of the Critical Value, the Critical (Rejection) Region(s), and the Test Statistic.
Use the following information for questions 7-11.
Given below are recorded weights, in pounds, of 18 randomly selected Sitka Elephant Seals.
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805
|
903
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809
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916
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615
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924
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825
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940
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650
|
|
635
|
940
|
540
|
598
|
988
|
993
|
899
|
936
|
937
|
Q7. What type of data are the values listed above?
A) Categorical
B) Qualitative
C) Numerical
D) None of These
Input the seal weight data as a list into your calculator.
The sum of your data, ∑x, should be 14853.
Q8. Write the 5 Number Summary for the data (show one significant figure after the decimal, round if necessary).
Minimum:
First Quartile:
Second Quartile (Median):
Third Quartile:
Maximum:
Q9. What is the mean of the sample data?
A) 940
B) 149.51
C) 825.17
D) None of These
Q10. What is the mode of the sample data?
A) 940
B) 149.51
C) 825.17
D) None of These
Q11. What is the standard deviation of the sample data?
A) 940
B) 149.51
C) 825.17
D) None of These
Use the following information to answer question 12.
In a 2016 Artful Dodger Survey, 565 randomly selected California college students were asked if they felt that U.S. relations with Britain were improving. 214 people responded "yes." The data collected has a binomial distribution.
Q12. The 80% confidence interval to estimate the true value of the population proportion, p, is:
A) (0.210, 0.320)
B) (0.353, 0.405)
C) (0.595, 0.647)
D) None of these.
Use the following information to answer questions 13 and 14.
Dominque has a dog treat jar that contains two flavors of treats for her dog Zeus. In the jar are 14 cheese-flavored treats and 5 basil-flavored treats. Dominique selects one treat out of the jar at random and gives it to Zeus. Zeus eats the treat and begs for another. Dominque selects a second treat at random and feeds it to Zeus. Zeus eats the second treat too.
Q13. Find the probability that Zeus eats two treats of the same flavor.
A) 0.560
B) 0.591
C) 0.612
D) None of These
Q14. Find the probability that Zeus gets at least one basil-flavored treat.
A) 0.338
B) 0.440
C) 0.468
D) None of These
Q15. Identify the Chi-Squared test statistic.
A) 0.243
B) 1
C) 1.364
D) None of these
Q16. Identify the P-Value.
A) 0.243
B) 1
C) 1.364
D) None of these
Q17. Based on your test, you
A) Reject H0
B) Foil to Reject H0
C) Neither of these
Q18. State your conclusion.
A) There is not sufficient evidence to warrant rejection of the claim that left-handedness is independent of the coast on which a person is born.
B) There is sufficient evidence to warrant rejection of the claim that left-handedness is independent of the coast on which a person is born.
C) Neither of these.
Use the following information to answer questions 19-23.
4 groups of sapling cinnamon trees were grown in dry woodland using different irrigation techniques and their weights recorded. Each group consisted of 5 equal age trees.
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Group
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Treatment Type
|
|
1
|
No Treatment
|
|
2
|
Water Only When Tree Appears Stressed from lack of Water
|
|
3
|
Twice a Month Deep Soaks
|
|
4
|
Daily Watering
|
Recorded Weights:
|
Group 1
|
Group 2
|
Group 3
|
Group 4
|
|
0.24
|
0.92
|
0.96
|
1.07
|
|
1.69
|
0.07
|
1.43
|
1.63
|
|
1.23
|
0.56
|
1.26
|
1.39
|
|
0.99
|
1.74
|
1.57
|
0.49
|
|
1.8
|
1.13
|
0.72
|
0.95
|
Check to see if you entered the data correctly:
|
Group
|
∑x
|
|
1
|
5.95
|
|
2
|
4.42
|
|
3
|
5.94
|
|
4
|
5.53
|
Use a one-way analysis of variance (ANOVA) to test the clean that the four treatment groups yield trees with the same mean weight. Use a significance level of 0.05
Q19. Identify your null hypothesis.
A) H0: σ1 = σ2 = σ3 = σ4
B) H0: μ1 = μ2 = μ3 = μ4
C) H0: At least one of the means is different from the others.
D) None of these.
Q20. Identify your alternative hypothesis.
A) H1: At least one of the means is different from the others
B) H1: All of the means are different from each other
C) H1: No more than two of the means are the same
D) None of these.
Q21. Identify the test statistic.
A) F = 0.7687
B) F = 0.3801
C) F = 0.5226
D) None of these
Q22. Identify the P-Value.
A) 0.7687
B) 0.3801
C) 0.5226
D) None of these
Q23. State your conclusion.
A) Reject H0
B) Fail to Reject H0
C) Neither of these.