Statistics Assignment -
Use the following information to answer the questions 1-11.
The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. All of the diamonds have the same rating of "very good." ∑x = 3.4 for the Weight data. ∑x = 10775 for the Price data.
|
Weight
|
0.3
|
0.45
|
0.5
|
0.65
|
.85
|
0.7
|
|
Price
|
510
|
1151
|
1343
|
1950
|
3444
|
2377
|
Q1. Create a scatter plot of the data with the Weight data on the horizontal axis. Identify the ordered pair wqith the highest value for the independent variable.
A) (0.7, 2377)
B) (0.85, 3444)
C) (3444, 0.85)
D) None of these
Q2. Does the data appear to be at least approximately linear?
A) No
B) Yes
Q3. Identify the type of correlation between the x and y coordinates.
A) Positive Correlation
B) Negative Correlation
C) No Correlation
Q4. Consider a Linear Regression T Test to test the claim that there is no correlation between two variables. Use a significance level of 0.05. Identify your null hypothesis.
A) H0 : ρ = 0
B) H0 : ρ ≠ 0
C) H0 : r =1
D) None of these
Q5. Identify your alternative hypothesis.
A) H1 : ρ = 0
B) H1 : ρ ≠ 0
C) H1 : r ≠ 1
D) None of these
Q6. Identify the P-Value.
A) 0.9752
B) 0.9875
C) 2.324E-4
D) None of these
Q7. State your conclusion.
A) Reject H0
B) Fail to Reject H0
C) Neither of these
Q8. Identify the linear correlation coefficient for the sample data.
A) 0.9752
B) 0.9875
C) 2.324E-4
D) None of these
Q9. Identify the y-intercept of the linear regression equation.
A) 5190.32
B) -1188.60
C) 1795.83
D) None of these
Q10. Identify the slope of the linear regression equation.
A) 5190.32
B) -1188.60
C) 1795.83
D) None of these
Q11. Assuming the regression equation is a good model, predict the price of a diamond of this class if its weight is 0.8 carats.
A) $4239.44
B) $2963.66
C) $1795.83
D) None of these
Use thy following information to answer questions 12-15.
Assume that Soliton wave heights are normally distributed with a mean of 150.8 feet and a standard deviation of 72.6 feet.
Q12. Find the probability that a randomly selected wave is greater than 200 feet,
A) 0.751
B) 0.578
C) 0.249
D) None of these
Q13. Find the probability that a randomly selected wave is between 65 and 90 feet.
A) 0.0825
B) 0.9174
C) 0
D) None of These
Q14. If you wean to consider only those waves in the top 15% what is the smallest height you can include?
A) 1.036
B) 226.045
C) 173.42
D) None of These
Q15. Find the z-score for a wave height of 145 feet.
A) -0.0799
B) -12.552
C) 2.077
D) None of These
Use the following information to answer questions 16 and 17.
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.
|
Group
|
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 claim that the four treatment groups yield trees with the same mean weight. Use a significance level of 0.05.
Q16. Identify the test statistic.
A) F = 0.7687
B) F = 0.3801
C) F = 0.5226
D) None of these
Q16. Select an appropriate outcome statement.
A) There is sufficient evidence to support the claim that there is no statistical difference in the mean tree weight between the groups.
B) There is insufficient evidence to support the claim that there is no statistical difference in the mean tree weight between the groups.
C) Neither of these.