Question

3. Eleven tires were each measured for treadwear by two methods, one based on weight and the other on groove wear. The following are the data, in thousands of miles. Weight method (?1) | Groove method (?2) | Difference ?1 - ?2 --- | --- | --- 30.5 | 28.7 | 1.8 30.9 | 25.9 | 5 31.9 | 23.3 | 8.6 30.4 | 23.1 | 7.3 27.3 | 23.7 | 3.6 20.4 | 20.9 | -0.5 24.5 | 16.1 | 8.4 20.9 | 19.9 | 1 18.9 | 15.2 | 3.7 13.7 | 11.5 | 2.2 11.4 | 11.2 | 0.2 ?x1 = 23.71, s1 = 7.19 | ?x2 = 19.95, s2 = 5.77 | ?d = 3.75, sd = 3.22 (a) Are the data two independent samples or a simple paired sample? (2 marks) (b) At the 5% significance level, do the data provide sufficient evidence to conclude that, on average, the two measurement methods give different results? (8 marks) (c) What is the P-value of the hypothesis test in part (b)? (2 marks) (d) Obtain and interpret a 95% two-sided confidence interval for the mean difference between measurements from the weight and groove methods. (6 marks) (e) Does the interval in (d) support the conclusion of the hypothesis test in part (b)? Justify your answer. (2 marks)

          3. Eleven tires were each measured for treadwear by two methods, one based on weight and the other on groove wear. The following are the data, in thousands of miles.

Weight method (?1) | Groove method (?2) | Difference ?1 - ?2
--- | --- | ---
30.5 | 28.7 | 1.8
30.9 | 25.9 | 5
31.9 | 23.3 | 8.6
30.4 | 23.1 | 7.3
27.3 | 23.7 | 3.6
20.4 | 20.9 | -0.5
24.5 | 16.1 | 8.4
20.9 | 19.9 | 1
18.9 | 15.2 | 3.7
13.7 | 11.5 | 2.2
11.4 | 11.2 | 0.2
?x1 = 23.71, s1 = 7.19 | ?x2 = 19.95, s2 = 5.77 | ?d = 3.75, sd = 3.22

(a) Are the data two independent samples or a simple paired sample? (2 marks)
(b) At the 5% significance level, do the data provide sufficient evidence to conclude that, on average, the two measurement methods give different results? (8 marks)
(c) What is the P-value of the hypothesis test in part (b)? (2 marks)
(d) Obtain and interpret a 95% two-sided confidence interval for the mean difference between measurements from the weight and groove methods. (6 marks)
(e) Does the interval in (d) support the conclusion of the hypothesis test in part (b)? Justify your answer. (2 marks)

3. Eleven tires were each measured for treadwear by two methods, one based on weight and the other on groove wear. The following are the data, in thousands of miles.

Weight method (?1) | Groove method (?2) | Difference ?1 - ?2
— | — | —
30.5 | 28.7 | 1.8
30.9 | 25.9 | 5
31.9 | 23.3 | 8.6
30.4 | 23.1 | 7.3
27.3 | 23.7 | 3.6
20.4 | 20.9 | -0.5
24.5 | 16.1 | 8.4
20.9 | 19.9 | 1
18.9 | 15.2 | 3.7
13.7 | 11.5 | 2.2
11.4 | 11.2 | 0.2
?x1 = 23.71, s1 = 7.19 | ?x2 = 19.95, s2 = 5.77 | ?d = 3.75, sd = 3.22

(a) Are the data two independent samples or a simple paired sample? (2 marks)
(b) At the 5% significance level, do the data provide sufficient evidence to conclude that, on average, the two measurement methods give different results? (8 marks)
(c) What is the P-value of the hypothesis test in part (b)? (2 marks)
(d) Obtain and interpret a 95% two-sided confidence interval for the mean difference between measurements from the weight and groove methods. (6 marks)
(e) Does the interval in (d) support the conclusion of the hypothesis test in part (b)? Justify your answer. (2 marks)

Added by Beatriz R.

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