# Statistics homework help

STAT 350 (Spring 2017) Homework 10 (20 points + 1 point BONUS) 1

Practice Problems: 11.1 (p. 540), 11.3 (p. 540), 11.5 (p. 540), 11.37 (p. 551), 11.41 (p.551) (1 pt. BONUS) 1. BONUS: Show that SST = SSE + SSA (2 pts.) 2. In each of the following problems, use the summary statistics and the Tukey

confidence intervals to construct the corresponding graph indicating which pairs of means are and are not significantly different. No work is required.

(1 pt.) a)

Sample means

x̄1. = 32.52 x̄2. = 35.05 x̄3. = 29.77

Difference Confidence interval

1 – 2 (-3.10, 8.16)

1 – 3 (-2.88, 8.38)

2 – 3 (-0.35, 10.91)

(1 pt.) b)

Sample means

x̄1. = 2.91 x̄2. = 6.57 x̄3. = 2.76 x̄4. = 4.63

Difference Confidence interval

1 – 2 (1.55, 5.77)

1 – 3 (-1.96, 2.26)

1 – 4 (-3.83, 0.39)

2 – 3 (1.70, 5.92)

2 – 4 (-0.17, 4.05)

3 – 4 (-3.98, 0.24)

(2 pts.) 3. In each of the following problems, the results from a multiple comparison procedure

are shown graphically. Use each illustration to identify all pairs of population means that are significantly different. No work is required.

(1 pt.) a)

x̄3. x̄1. x̄2. x̄4. 58.98 62.59 62.62 70.64

(1 pt.) b)

x̄3. x̄4. x̄2. x̄1. -1.62 -1.50 -1.39 -1.10

STAT 350 (Spring 2017) Homework 10 (20 points + 1 point BONUS) 2

(16 pts.) 4. Breitling sells men’s gold, silver, and titanium watchbands. A random sample of each type was obtained (in similar styles), and the weight of each watchband (in grams) was recorded. The following table provides the summary data.

Metal Gold Silver Titanium

n 8 8 8

x̄ 8.16 7.97 6.05

s 0.840 1.037 1.165

(1 pt.) a) Is the constant standard deviation assumption valid in this case? Please explain your

answer. (4 pts.) b) Fill in the following ANOVA table given the information below. Remember work is

required for each box in the table.

Source of Variation

Degrees of freedom

Sum of squares

Mean square F

Factor 10.9 Error 21.99

Total (5 pts.) c) Assuming that the populations are normal, is there any evidence to suggest that the

average weight of at least two of watchband types are different? Use = 0.01. Perform the complete 4-step summary. Be sure to include the two degrees of freedom necessary to calculate the p-value. You may use the numbers calculated above in part b), without reshowing your work.

(4 pts.) d) Construct the Tukey 99% confidence intervals to isolate the pairs of means contributing to the overall difference. For each pair indicate whether the two means are different or not.

(1 pt.) e) Draw a diagram to represent the results of the multiple comparison procedure in part d).

(1 pt.) f) If you are trying to find the heaviest of the watchbands, which metal(s) should you use? Explain your answer.

Section 11.1: There are no problems that have you generate the ANOVA table from the

summations and use that to conduct the ANOVA hypothesis test, the problems also have you calculate the sums. However, the ANOVA tables are in the back of the book.

Additional Problems: 11.15, 11.17, 11.21 Section 11.2: The only odd problem that uses the Tukey method doesn’t provide the MSE of

sample sizes in the problem, therefore the Additional Problems use the Bonferroni method. Additional Problems: 11.49, 11.53

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