Stat 200 Week 7 Homework
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Week 7
2.
The formula for a regression equation is Y’ = 2X + 9.
a. What would be the predicted score for a person scoring 6 on X?
b. If someone’s predicted score was 14, what was this person’s score on X?
6.
For the X, Y data below, compute:
a. r and determine if it is significantly different from zero.
5.
At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it is a little fishy that sophomores organized the raffle and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors.
(a) What are the expected frequencies of winners from each class?
(b) Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values.
(c) What do you conclude?
14.
A geologist collects hand-specimen sized pieces of limestone from a particular
Area. A qualitative assessment of both texture and color is made with the
Following results. Is there evidence of association between color and texture for?
These limestones? Explain your answer.
70.
The standard deviation of the chi-square distribution is twice the mean.
102.
Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance.
Freedom Toast
Pancakes
Waffles
Omelettes
Men
47
35
28
53
Women
65
59
55
60
Use the following information to answer exercises seven and eight:
Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.
103.
df = ___24_____
117.
Let α = 0.05 Decision: ________ Conclusion (write out in a complete sentence.): ________
Solution:
We states our hypotheses as
H0: σ2 ≥ 150
H1: σ2 ≤ 150
Level of significance: α = 5% = 0.05
Test statistics:
Χ2 =
=
=
= 36
Critical region:
Χ2 < Χ2(1-σ/2)
36 < 13.848
Conclusion:
Since the calculated value of chi-square is greater than the critical value of chi-square = 13.848. So we accept H0 at 5% level of significance and and there is insufficient evidence.
66.
Can a coefficient of determination be negative? Why or why not?
Solution:
No because the ratio of the explained variation to the total variation is called the coefficient of determination. Since the ratio is always non negative because it is positive square of the correlation coefficient.
If the total variation is all explained,the ratio r2 is one.on the other hand,if the total variation is all unexplained,then the explained variation and the ratio r2 is zero.in other cases the ratio r2 is lies b/w 0 and 1.the square root of the co_efficient of determination is called the co_efficient of correlation.
r =
r = ±
Use the following information to answer exercises 10. The cost of a leading liquid laundry detergent in different sizes is given in Table 12.31.
Size (ounces)
Cost ($)
Cost per ounce
16
3.99
0.2494
32
4.99
0.1559
64
5.99
0.0936
200
10.99
0.0550
82.
a. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatter plot.
A scatter plot is the only way to determinr whether or not a relationship b/w two variables exists,is to plot each pair of independent dependent observations as a point on graph paper,using the x_axis for the regression variable and the Y_axis for the dependent variable.The scatter plot is shown below,
<
[Solved] Stat 200 Week 7 Homework
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- Ashleigh
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Week 7 2. The formula for a regression equation is Y’ = 2X + 9. a. What would be the predicted score for a person scoring 6 on X? b. If someone’s predicted score was 14, what was this person’s score on X? Solution As we have given that, y^'=2x+9 We need to predict the score at X =6, as y^'=2*6+9 y^'=12+9 y^'=21 b) If y^'=14 then the persons scores on X is, y^'=2x+9 14=2x+9 14-9=2x 5=2x x=5/2 x=2.50 6. For the X, Y data below, compute: r and determine if it is significantly different from zero. Solution: We state our hypothesis as, H0: ρ=0 H1: ρ≠0 Level of significance: α = 5% = .05 Test statistics are: t = (r√(n-2))/√(1-r^2 ) t = 0.85*√(6-2)/√(1-〖0.85〗^2 ) t=0.85*√4/√0.2775 t=0.85*2/0.5268 t = 3.23 Critical region: | t| ≥ tα/2, v Where v = n-1 degree of freedoms V = 6-1 V = 5 3.23≥ 2.776 Conclusion: Since the calculated value of t is greater than the critical value of t so we reject H0 at 5% level of significance. b. the slope of the regression line and test if it differs significantly from zero. c. the 95% confidence interval for the slope. X Y 4 6 3 7 5 12 11 17 10 9 14 21 Solution of b and c): Regression Analysis r² 0.721 n 6 r 0.849 k 1 Std. Error 3.503 Dep. Var. y ANOVA table Source SS df MS F p-value Regression 126.9207 1 126.9207 10.34 .0324 Residual 49.0793 4 12.2698 Total 176.0000 5 Regression output confidence interval variables coefficients std. error t (df=4) p-value 95% lower 95% upper Intercept 3.1231 3.1085 1.005 .3719 -5.5075 11.7537 x 1.1332 0.3523 3.216 .0324 0.1550 2.1115 5. At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it is a little fishy that sophomores organized the raffle and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors. (a) What are the expected frequencies of winners from each class? (b) Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values. (c) What do you conclude? Solution: We states our hypotheses as H0: The fit is good. H1: The fit is not good. Level of significance: α = 0.05(5%) Critical region: Χ2 > Χ20.05 and Χ2 < Χ20.95 for v = (r-1) (c-1) degree of freedom. Test statistics: Χ2 = ∑▒(E-0)^2/E The expected frequencies are calculated by the number of scores by the proportion. The final column shows the observed number of scores in the range, it is clear that the observed frequencies very greatly from the expected frequencies. serials Observed Proportion Expected (E-...
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