Let mu_1 and mu_2 denote true average densities for two different types of brick
ID: 3234029 • Letter: L
Question
Let mu_1 and mu_2 denote true average densities for two different types of brick. Assuming normality of the two density distributions, test H_0: mu_1 - mu_2 = 0 versus H_a: mu_1 - mu_2 notequalto 0 using the following data: n_2 = a, x_1 = 22.71, s_1 = 0.164, n_2 = 4, x_2 = 21.99. and s_2 = 0.240. The degrees of freedom according to the satterthwalte approximation are: df = Use alpha = 0.05. Round your test statistic to three decimal places and your P-value to four decimal places.) Use the satterthwalte degrees of freedom for your p-value. t - P-value - State the conclusion in the problem context. Reject H_0. The data provides no evidence of a difference between the true average densities for the two different types of brick. Fall to reject H_0. The data provides no evidence of a difference between the true average densities for the two different types of brick. Fall to reject H_0. The data provides convincing evidence of a difference between the true average densities for the two different types of brick. Reject H_0. The data provides convincing 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 mu = mu_2 are: (Use the satterthwalte degrees of freedom for your critical value.) You may need to use the appropriate table in the Appendix of Tables to answer this question.Explanation / Answer
df = n1 + n2 - 2 = 8 + 4 -2 = 10
x1 = 22.71 , x2 = 21.99 , s1 = 0.164 , s2 = 0.240 , n1 = 8 , n2 = 4
SE = sqrt[(s1^2/n1) + (s2^2/n2)]
SE = sqrt[(0.164^2/8) + (0.240^2/4)]
= 0.133
t = [ (x1 - x2) - d ] / SE
= [ (22.71 - 21.99) - 0 ] / 0.133
= 5.4135
P value is calcuulated using t = 5.4135 , df = 10
P value = .000296.
Reject H0 . The data provides convincing evidence of a difference between the true average
Point estimate = x1 - x2 = 22.71 - 21.99 = 0.71
t value at 95% CI = 2.228
ME = t * sqrt ( s1^2 / n1 + s2^2/n2)
= 2.228 * sqrt[(0.164^2/8) + (0.240^2/4)]
= 0.2969
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