Investment A has an expected return of 8% with a standard deviation of 2.5%.
Investment B has an expected return of 6% with a standard deviation of 1.2%. Assume
you invest equally in both investments and that the rates of return are independent.
What is the standard deviation of the return on your portfolio? Assume that the returns
on the two investments are independent.
2.5
2.77
6.25
7.69
Unable to determine the relationship between expression 1 and expression 2.
Value of expression 2 is greater than value of expression 1.
Value of expression 1 is greater than value of expression 2.
Value of expression 1 is equal to value of expression 2.
Your state is considering raising the legal age for consumption of alcoholic beverages
to 21 years old. How large a sample size must be taken to make an estimate of the true
proportion of citizens who favor this move, if the error should be no more than 0.01
with 99% confidence?
16577
9604
6540
13573
A local transportation planning group is concerned about the lack of car-pooling on the
part of commuters. They are afraid that the proportion of local drivers car-pooling is
below the national average of 20%. What are the appropriate null and alternative
hypotheses?
H0 : μ > 0.20 and H1 : μ ≤ 0.20
H0 : μ = 0.20 and H1 : μ ≠ 0.20
H0 : μ = 0.20 and H1 : μ < 0.20
H0 : μ = 0.20 and H1 : μ > 0.20
Suppose you have the following null and alternative hypotheses: H0 : σ = 34.5 and
H0 : σ > 34.5 . You take a random sample of 15 observations and find that s = 48.1 .
What is the most accurate statement that you can make about the p-value for this test?
p-value < 0.10
p-value < 0.025
p-value < 0.01
p-value < 0.05
A tortilla chip manufacturer claims that, on average, they put 16.1 ounces of chips in
each bag they produce. However, due to variations in chip size, the standard deviation
of the weight of chips in bags is 0.35 ounces. A consumer group buys 40 bags of chips
and weighs them. They find the sample mean to be 15.9 ounces. Which of the
following statements is true?
We cannot tell if the manufacturer is telling the truth since the sample size is only
40.
The manufacturer may be telling the truth. The probability of a sample mean of
15.9 or less is 0.095.
It is virtually impossible to get this result if the manufacturer is telling the truth.
The manufacturer may be telling the truth. The probability of a sample mean of
15.9 or less is 0.284.
The lower limit of a confidence interval at the 95% level of confidence for the
population proportion if a sample of size 200 had 40 successes is:
0.1535
0.2554
0.1446
0.2465
As shift manager at a local fast food place, you are responsible for ensuring quality
control. You do not want to weigh all the frozen hamburger patties that get delivered
by your supplier to make sure they weigh four ounces on average, so you have one of
your minimum wage earners do it. Assume that the standard deviation of the weight of
hamburger patties is known to be 0.1 ounces. You tell your employee that as a
shipment comes in, select 20 patties at random. Find the average weight for the 20
patties. If the average weight is less than 3.95 ounces, reject the shipment. What is the
significance level associated with your decision rule?
0.023
0.015
0.013
0.008
Which of the following statements is not true?
In determining the necessary sample size in making an interval estimate for a
population mean, it may be necessary to first make an estimate of the population
standard deviation
If we want to cut the tolerable width of a confidence interval in half, we will have
to double the sample size.
None of the above
An assembly line will be shut down for maintenance if the defect rate exceeds 2.3%.
Suppose you adopt a 5% significance level and take a random sample 200 items off the
assembly line and compute the proportions that are defective. For what values of the
sample proportion will the assembly line be shut down?
0.036
0.034
0.038
0.04
In reference to the Durbin. Watson statistic d and the critical values dL and dU ,
which of the following statements is false?
If d < 4 − dU , we conclude that there is not enough evidence to show that negative
first order autocorrelation exists.
If dU ≤ d ≤ 4 − dU , we conclude that there is no evidence of first order
autocorrelation.
If d > 4 − dL , we conclude that the negative first order autocorrelation exists.
None of the above.
A large mail house which mails such items as catalogues, magazines, and other bulk
mailings guarantees that there will be no more than a 3% error rate on its mailing
labels. A customer who contracted a mailing to 190,000 individuals experienced a
return of 5,900 items, which had incorrect addresses. Using what you have learned
concerning the probability of 6000 incorrect addresses, do you think that the mail
house has lived up to its guarantee?
There is a 2.69 percent possibility that a return of 5900 incorrect addresses could
occur if the true error rate is 3%.
There is a 0.496 probability that a return of 5900 incorrect addresses could occur if
the true error rate is 3%.
There is a 3% chance of an incorrect return.
There is a 0.004 probability that a return of 5900 incorrect addresses could occur if
the true error rate is 3%.
A sample of 25 bottles is taken from the production line at a local bottling plant.
Assume that the fill amounts follow a normal distribution. Which of the following
statements is the most accurate estimate of the probability that the sample standard
deviation is more than 40% of the population standard deviation?
The probability is smaller than 0.995.
The probability is smaller than 0.95.
The probability is greater than 0.995.
The probability is smaller than 0.975.
You have recently joined a country club. The number of times you expect to play golf
in a month is represented by a random variable with a mean of 10 and a standard
deviation of 2.2. Assume you pay monthly membership fees of $500 per month and
pay and additional $50 per round of golf. What is the standard deviation for your
average monthly bill from the country club?
180
110
324
220
Because of the popularity of movies as an entertainment medium for college students,
you plan to do a national study of the average cost of a movie ticket. If you assume that
σ = $0.50 , what sample size would you have to take to be 95% confident that your
estimate was within $0.25 of the true mean ticket prices?
7
8
16
15
Investment A has an expected return of 7.8% with a standard deviation of 2%.
Investment B has an expected return of 7.2% with a standard deviation of 3.1%.
Assume the returns on both of these stocks are normally distributed. Which stock is
more likely to have a return greater than 10%?
Stock A
Stock B
The probability is the same for both A and B .
Unable to determine
The manufacturer of bags of cement claims that they fill each bag with at least 50.2
pounds of cement. Assume that the standard deviation for the amount in each bag is
1.2 pounds. The decision rule is adopted to shut down the filling machine if the sample
mean weight for a sample of 40 bags is below 49.8. Suppose that the true mean weight
of bags is 50 pounds. Using this decision rule, what is the probability of a Type II
error?
0.85
0.75
0.8
0.7
An office of six people is plagued by high absenteeism. It is thought that the
probability than an employee is absent on a particular day is 0.03. Assuming that the
event that one person is absent on a particular day is independent of the absence of any
other employee, what is the probability that at least one employee is absent tomorrow?
0.18
0.167
0.121
0.15
In a recent survey about US policy in Iraq, 62% of the respondents said that they
support US policy in Iraq. Females comprised 53% of the sample, and of the females,
46% supported US policy in Iraq. A person is selected at random. What is the
probability that the person we select is female and support US policy in Iraq?
Define the followings in words:
(1) 99% confidence interval
(2) Sampling distribution of sample mean with n = 20
Please indicate if each of the following statements about the simple linear regression
model is true or false and explain why. Note that no credit will be rewarded without any
explanation no matter the answer is true or false. (20%)
(一) The simple regression line estimated by the method of Least Square passes through
the sample mean of dependent and independent variable. (4%)
(二) The sample covariance between the residuals from the least square regression and
the explanatory variable is zero.(4%)
(三) If the values of x more widely spread out, the estimate of the slope coefficient is
less concise.(4%)
(四) “t-statistics is used while conducting the hypothesis testing of the slope coefficient”
is based on the assumption of normality of the error term.(4%)
(五) If the slope estimator of the Least Squares Regression line is zero, the explained
sum of square is zero.(4%)
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