Question

QUESTION 7 Questions 6 - 10 concern the following idea: The CEO of a company is trying to decide between two different suppliers of recycled aluminium (Alumania and Beautinium), she is not sure which one is better so is testing for a difference in either direction. She has decided to go with the supplier that has the smallest average impurities. 35 samples are obtained from each supplier and in each sample the percentage of impurity is measured. The results were analyzed in R via a 2-sample t-test with a 2-sided alternative hypothesis, and some of the output is summarized below (assume ? = 0.05 where necessary). mean sd n Alumania 3.67 3.34 35 Beautinium 4.01 3.74 35 Two Sample t-test data: impurity by supplier t = -0.413, df = 68, p-value = 0.6895 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -2.03 1.35 Levene's Test for Homogeneity of Variance (center = "median") Df F value Pr(>F) group 1 0.1977 0.658 68 Let ?1 and ?2 denote the mean amount of impurities from the suppliers "Alumania" and "Beautinium" respectively, and ?1² and ?2² be the respective variances. What is the pooled estimate of the standard deviation (correct to 3dp)?

          QUESTION 7

Questions 6 - 10 concern the following idea: The CEO of a company is trying to decide between two different suppliers of recycled aluminium (Alumania and Beautinium), she is not sure which one is better so is testing for a difference in either direction. She has decided to go with the supplier that has the smallest average impurities. 35 samples are obtained from each supplier and in each sample the percentage of impurity is measured.

The results were analyzed in R via a 2-sample t-test with a 2-sided alternative hypothesis, and some of the output is summarized below (assume ? = 0.05 where necessary).

              mean    sd    n
Alumania      3.67  3.34   35
Beautinium    4.01  3.74   35

Two Sample t-test
data: impurity by supplier
t = -0.413, df = 68, p-value = 0.6895
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-2.03 1.35

Levene's Test for Homogeneity of Variance (center = "median")
        Df  F value  Pr(>F)
group    1   0.1977   0.658
        68

Let ?1 and ?2 denote the mean amount of impurities from the suppliers "Alumania" and "Beautinium" respectively, and ?1² and ?2² be the respective variances.

What is the pooled estimate of the standard deviation (correct to 3dp)?

QUESTION 7

Questions 6 - 10 concern the following idea: The CEO of a company is trying to decide between two different suppliers of recycled aluminium (Alumania and Beautinium), she is not sure which one is better so is testing for a difference in either direction. She has decided to go with the supplier that has the smallest average impurities. 35 samples are obtained from each supplier and in each sample the percentage of impurity is measured.

The results were analyzed in R via a 2-sample t-test with a 2-sided alternative hypothesis, and some of the output is summarized below (assume ? = 0.05 where necessary).

mean sd n
Alumania 3.67 3.34 35
Beautinium 4.01 3.74 35

Two Sample t-test
data: impurity by supplier
t = -0.413, df = 68, p-value = 0.6895
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-2.03 1.35

Levene's Test for Homogeneity of Variance (center = "median")
Df F value Pr(>F)
group 1 0.1977 0.658
68

Let ?1 and ?2 denote the mean amount of impurities from the suppliers "Alumania" and "Beautinium" respectively, and ?1² and ?2² be the respective variances.

What is the pooled estimate of the standard deviation (correct to 3dp)?

Added by Steven S.

Question

Please give Ace some feedback