Question

Suppose 31.34% of small businesses experience cash flow problems in their first 5 years. A consultant takes a random sample of 637 businesses that have been opened for 5 years or less. What is the probability that greater than 30.86% of the businesses have experienced cash flow problems?

Question 2 options:

	1) -19.9782
	2) 0.5000
	3) 0.6030
	4) >0.999
	5) 0.3970

Question 3 (1 point)

You are contacted by a phone-in technical support business that is interested in some information about the amount of time their customers spend on hold. You find out that on average, each caller spends 7.57 minutes on hold with a standard deviation of 1.67 minutes. If you were to take a random sample of 64 callers, you would expect 41% of the time the average hold time would be greater than how many minutes?

Question 3 options:

	1) 7.19
	2) 7.62
	3) There is not enough information to determine this.
	4) 7.95
	5) 7.52

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 25 participants on the drug had an average test score of 24 (SD = 4.644) while those 27 participants not on the drug (taking the placebo) had an average score of 26.49 (SD = 4.609). 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: -1.939, P-Value: 0.9709
	2) Test Statistic: 1.939, P-Value: 0.9709
	3) Test Statistic: -1.939, P-Value: 0.0291
	4) Test Statistic: 1.939, P-Value: 0.0291
	5) Test Statistic: -1.939, P-Value: 0.0582

Answer 1

2)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.3134
sample size       =n=	637
std error of proportion=σp=√(p*(1-p)/n)=	0.0184

probability =

P(X>0.3086)

=

P(Z>-0.26)=

1-P(Z<-0.26)=

1-0.397=

0.6030

3)

std error=σx̅=σ/√n=

0.2088

for 59th percentile critical value of z=		0.23
therefore corresponding value=mean+z*std deviation=			7.62

4)

pool. var S2p=

((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=

21.3983

Point estimate :		x1-x2                                     =	-2.4900
std error of difference=Se=		Sp*√(1/n1+1/n2)		=	1.284
test stat t =		(x1-x2-Δo)/Se		=	-1.939

correct option is 3) Test Statistic: -1.939, P-Value: 0.0291