5.8) Stats Let 1 and 2 denote true average densities for two different types of
ID: 2935829 • Letter: 5
Question
5.8) Stats
Let 1 and 2 denote true average densities for two different types of brick. Assuming normality of the two density distributions, test: Ho: 1-2 = 0 versus Hai 1_2 # 0 Use the following data: n1 = 8, x1 = 23.71, s1 = 0.161, n2 = 7, x2 = 20.97, and s2 = 0.250. The degrees of freedom according to the satterthwaite approximation are: (Round down to nearest whole number.) df = Use = 0.05. Round your test statistic to three decimal places and your P-value to four decimal places.) Use the satterthwaite degrees of freedom for your p-value. P-value State the conclusion in the problem context. Fail to reject Ho. The data provides convincing evidence of a difference between the true average densities for the two different types of brick. Reject Ho. The data provides convincing evidence of a difference between the true average densities for the two different types of brick. O Reject Ho. The data provides no evidence of a difference between the true average densities for the two different types of brick. Fail to reject Ho. The data provides no evidence of a difference between the true average densities for the two different types of brick. The point estimate and margin of error for the 95% confidence interval for 1-12 are: (Use the satterthwaite degrees of freedom for your critical value.)Explanation / Answer
Solution:
From the given information
n1 = 8 n2 = 7
x1 = 23.71 x2 = 20.97
s1 = 0.161 s2 = 0.250
Test Hypothesis:
H0: 1-2 = 0
Ha: 1-2 0
Degrees of freedom = n1+ n2-2
= 8+ 7-2 = 13
Assume that the level of significance is 0.05
Test statistic t = x1 - x2/ sqrt(s1^2/n1+s2^2/n2)
= 23.72 - 20.97 /sqrt((0.161)^2/8 + (0.250)^2/7)
= 24.92
P-value: 0.0001
The point estimate of the difference of means 'Point estimate = x1-x2
= 23.71-20.97 = 2.74
The critical value of t for 13 degrees of freedom and 5% level of significance is 2.160
Now calculate the margin of error
E = t(sqrt(s1^2/n1+s2^2/n2))
= (2.160 )(sqrt((0.161)^2/8 + (0.250)^2/7)
= (2.160 )(0.1103)
= 0.2382
Calculate the 95% confidence interval
CI = x1-x2 ± E
= 2.74 ± 0.2382
= (2.5018, 2.9782)
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