Question

Question 7 of 10 (5 points) | Attempt 1 of 1 | View question in a popup | © 2h 50m Remaining 11.3 Section Exercise 10 (critical value, table) ol. Comparing scales: In an experiment to determine whether there is a systematic difference between the weights obtained with two different scales, 10 rock specimens were weighed, in grams, on each scale. The following data were obtained: Specimen Weight on Scale 1 Weight on Scale 2 12.58 12.17 2 15.22 15.13 3 9.00 9.10 4 11.03 11.15 5 25.29 25.52 6 10.25 10.09 7 15.22 15.14 8 7.38 7.43 9 13.39 13.57 10 21.32 21.57 Send data to Excel Letų, represent the mean weight on Scale 1 and d =ļi -u2. Can you conclude that the mean weight differs between the Scales? Use the a=0.10 level of significance. Part: 0 / 5 Next Part Submit Assignment

Answer 1

Solution:

The following table is obtained:

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	12.58	12.17	0.41
	15.22	15.13	0.09
	9	9.1	-0.1
	11.03	11.15	-0.12
	25.29	25.52	-0.23
	10.25	10.09	0.16
	15.22	15.14	0.08
	7.38	7.43	-0.05
	13.39	13.57	-0.18
	21.32	21.57	-0.25
Average	14.068	14.087	-0.019
St. Dev.	5.559	5.643	0.205
n	10	10	10

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested: Hopp = 0 Hai Mp *0 This corresponds to a two-tailed test, for which a t-test for two paired samples be used. (2) Rejection Region Based on the information provided the significance level is a = 0.10, and the degrees of freedom are df = 9 Hence, it is found that the critical value for this two-tailed test is te = 1.833, for a = 0.10 and df = 9 SD The rejection region for this two-tailed test is R = {t : t > 1.833} (3) Test Statistics The t-statistic is computed as shown in the following formula: -0.019 0.293 0.205/v10 (4) Decision about the null hypothesis Since it is observed that t = 0.293 <te = 1.833, it is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p = 0.7764, and since p = 0.7764 > 0.10, it is concluded that the null hypothesis is not rejected.

Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the

mean weight differs between the scales  at the 0.10 significance level.