Question

A pharmaceutical company is testing a new drug to increase memorization ability. It takes a sample of individuals and splits them randomly into two groups: group 1 takes the drug, group 2 takes a placebo. After the drug regimen is completed, all members of the study are given a test for memorization ability with higher scores representing a better ability to memorize. Those 21 participants on the drug had an average test score of 21.85 (SD = 4.22) while those 28 participants not on the drug (taking the placebo) had an average score of 20.94 (SD = 6.504). You use this information to perform a test for two independent samples with hypotheses Null Hypothesis: μ1 = μ2, Alternative Hypothesis: μ1 ≠ μ2. What is the test statistic and p-value? Assume the population standard deviations are equal. Question 14 options: 1) Test Statistic: -0.558, P-Value: 0.5795 2) Test Statistic: 0.558, P-Value: 0.2898 3) Test Statistic: 0.558, P-Value: 0.7103 4) Test Statistic: 0.558, P-Value: 0.5795 5) Test Statistic: 0.558, P-Value: 1.7103

As of 2012, the proportion of students who use a MacBook as their primary computer is 0.36. You believe that at your university the proportion is actually greater than 0.36. The hypotheses for this test are Null Hypothesis: p ≤ 0.36, Alternative Hypothesis: p > 0.36. If you randomly select 20 students in a sample and 10 of them use a MacBook as their primary computer, what is your test statistic and p-value?

Question 11 options:

	1) Test Statistic: 1.304, P-Value: 0.192
	2) Test Statistic: -1.304, P-Value: 0.096
	3) Test Statistic: 1.304, P-Value: 0.904
	4) Test Statistic: 1.304, P-Value: 0.096
	5) Test Statistic: -1.304, P-Value: 0.904

In a packing plant, one of the machines packs jars into a box. A sales rep for a packing machine manufacturer comes into the plant saying that a new machine he is selling will pack the jars faster than the old machine. To test this claim, each machine is timed for how long it takes to pack 10 cartons of jars at randomly chosen times. Given a 95% confidence interval of (0.72, 6.72) for the true difference in average times to pack the jars (old machine - new machine), what can you conclude from this interval?

Question 8 options:

	1) We are 95% confident that the average packing time of the old machine is greater than the new machine. The sales rep appears to be correct.
	2) We do not have enough information to make a conclusion.
	3) There is no significant difference between the average packing times of the two machines. The sales rep does not appear to be telling the truth.
	4) We are 95% confident that the difference between the two sample means falls within the interval.
	5) We are 95% confident that the average packing time of the new machine is greater than the old machine. The sales rep does not appear to be telling the truth.

Answer 1

14)

Pooled Variance Sp2=((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=				31.8792
Pooled Std dev Sp=√((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=				5.6462
Point estimate : x1-x2=			0.9100
standard error se =Sp*√(1/n1+1/n2)=			1.630
test stat t =(x1-x2-Δo)/Se=		0.558

Correct option is:

4) Test Statistic: 0.558, P-Value: 0.5795

11)

sample success x   =		10
sample size          n    =		20
std error   se =√(p*(1-p)/n) =		0.1073
sample proportion p̂ = x/n=		0.5000
test stat z =(p̂-p)/√(p(1-p)/n)=		1.30
p value                          =		0.096

option 4)

8)

since interval values are above 0;

We are 95% confident that the average packing time of the old machine is greater than the new machine. The sales rep appears to be correct.