Question

Question 2) Which of the following is true?
a) The significance level of a test is the probability that the null hypothesis is false.
b) The power of a test is the probability of accepting a null hypothesis that is true.
c) If a null hypothesis is rejected against an alternative at the 5% level, then using the same data, it must be rejected against that alternative at the 1% level.
d) If a null hypothesis is rejected against an alternative at the 1% level, then using the same data, it must be rejected against the alternative at the 5% level.
e). The p-value of a test is the probability that the null hypothesis is true.

Question 4) Which of the following is not true?
a) A narrower confidence interval for a population parameter with a given confidence level can be obtained by increasing the sample size.
b) The normal distribution is used to develop a confidence interval estimate of the population proportion if the sample size is large.
c) The value of the standard error of the mean is determined by dividing the total error by the sample size.
d) An estimator is unbiased if the mean of its sampling distribution is the population parameter being estimated.
e) none of the above

Question 15) The chairman of the statistics department in a certain college believes that 70% of the department’s graduate assistantships are given to international students. A random sample of 50 graduate assistants is taken. What is the probability that the sample proportion will NOT be between 0.60 and 0.73?
a) 0.61546
b) 0.3845
c) 0.45659
d) 0.5434
e) none of the above

Question 16) Each member of a random sample of 20 business economists was asked to predict the rate of inflation for the coming year. Assume that the predictions for the whole popu- lation of business economists follow a normal distribution with standard deviation 2%. Find any pair of values such that the probability that the sample standard deviation lies between these values is 0.90.

a) 1.459% and 2.519% b) 1.268% and 2.690% c) 1.176% and 2.774% d) 1.042% and 2.925% e) none of the above

Question 20) A sample of 30 students is taken from a college. These students spent an average of $175 on books this semester, with a sample standard deviation of $25. A 99% confidence interval for the average amount of money spent on books for all the college students equal to
a) 175 ± 10.872
b) 175 ± 12.579
c) 175 ± 8.946
d) 175 ± 6.329
e) none of the above

Answer 1

2)

d) If a null hypothesis is rejected against an alternative at the 1% level, then using the same data, it must be rejected against the alternative at the 5% level.

3)

c) The value of the standard error of the mean is determined by dividing the total error by the sample size

15)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.7000
sample size       =n=	50
std error of proportion=σp=√(p*(1-p)/n)=	0.0648

probability =1-P(0.6<X<0.73)=1-P((0.6-0.7)/0.065)<Z<(0.73-0.7)/0.065)=1-P(-1.54<Z<0.46)=1-(0.6772-0.0617)=0.3845

16)

	here n =	20
	s2=	4.000
Critical value of chi square distribution for n-1=19 df and 90 % CI
Lower critical value χ2L=		10.117
Upper critical valueχ2U=		30.144

for Confidence interval of standard deviation:
Lower bound =√((n-1)s2/χ2U)=		1.588
Upper bound =√((n-1)s2/χ2L)=		2.741

e) none of the above

20)

sample mean 'x̄=	175.000
sample size   n=	30.00
sample std deviation s=	25.00
std error 'sx=s/√n=	4.5644

for 99% CI; and 29 df, value of t=		2.756
margin of error E=t*std error    =		12.579

b) 175 ± 12.579