Download 1. An estimator is called consistent if its variance and standard

1. An estimator is called consistent if its variance and standard deviations consistently remain the same
regardless of changes in the sample size.
True
False
2. When determining the sample size n, if the value found for n is 79.2, we would choose to sample 79
observations.
True
False
3. The larger the p-value, the more the chance of rejecting the null hypothesis.
True
False
4. A fastener manufacturing company uses a chi-square goodness of fit test to determine if a population of
all lengths of ¼ inch bolts it manufactures is distributed according to a normal distribution. If we reject the
null hypothesis, it is reasonable to assume that the population distribution is at least approximately normally
distributed.
True
False
5. The chi-square distribution is a continuous probability distribution that is skewed to the left.
True
False
6. The error term in the regression model describes the effects of all factors other than the independent
variables on y (response variable).
True
False
7. When constructing a confidence interval for a sample proportion, the t distribution is always appropriate if
the sample size is small.
True
False
8. When the level of confidence and sample standard deviation remain the same, a confidence interval for a
population mean based on a sample of n=100 will be narrower than a confidence interval for a population
mean based on a sample of n=50.
True
False
9. The sampling distribution of the sample mean is always normally distributed according to the Central Limit
Theorem.
True
False
10. The error term is the difference between the observed value of the dependent variable and the predicted
value of the dependent variable.
True
False
11. We do not need to perform the continuity correction if the population is 20 times or more than the
sample size.
True
False
12. For a continuous distribution, Probability of (X greater than or equal to 10) is less than the probability of
(X greater 10)
True
False
13. In a regression model the population of potential error terms is assumed to have a t-distribution.
True
False
14. The least squares simple linear regression line minimizes the sum squares of the vertical deviations
between the line and the data points.
(Points : 8)
True
False
15. In testing the difference between two means from two independent populations, the sample sizes do not
have to be equal to be able to use the Z statistic.
True
False
16. To investigate the rate at which employees with cancer are fired or laid off, a telephone survey was
taken of 100 cancer survivors who worked while undergoing treatment. Seven (7) were either fired or laid
off due to their illness. Construct a 90% confidence interval for the true percentage of all cancer patients
who are fired or laid off due to their illness.
[0.0000 0.2034]
[0.0371 0.1029]
[0.0039 0.1361]
[0.0078 0.1400]
[0.0278 0.1122]
17. The area under the normal curve between z=2 and z=3 is ________________ the area under the
normal curve between z=1 and z=2.
Greater than
Less than
Equal to
Answers 1, 2, or 3 depending on the value of the Mean
Answers 1, 2, or 3 depending on the value of the Standard Deviation
18. For a given multiple regression model with three independent variables, the value of the adjusted
multiple coefficient of determination is _________ less than R .
Always
Sometimes
Never
Can be greater or less depending on the standard error
19. A new company is in the process of evaluating its customer service. The company offers two types of
sales: 1. Internet sales; 2. Store sales. The marketing research manager believes that the Internet sales are
more than 10% higher than store sales. The null hypothesis would be:
Pinternet-Pstore>.10
Pinternet-Pstore<.10
Pinternet-Pstore >=.10
Pinternet-Pstore <=.10
Pinternet-Pstore=.10
20. If a population distribution is known to be normal, then it follows that:
The sample Mean must equal the population mean
The sample Mean is skewed for small samples but becomes more and more normal as sample size increases
The sample Standard Deviation must equal the population standard deviation
The Sample Proportion must equal the population Proportion
None of the above
21. One survey conducted by a major leasing company determined that the Lexus is the favorite luxury car
for 25% of leases in Atlanta. Suppose a US car manufacturer conducts its own survey in an effort to
determine if this figure is correct. Of the 384 leases in Atlanta surveyed, 79 lease a Lexus. Calculate the
appropriate test statistic to test the hypotheses.
-2.15
-2.00 (Some would also consider -2.00 as a second correct value)
-0.91
2.00
2.51
22. The Ohio Department of Agriculture tested 203 fuel samples across the state in 1999 for accuracy of the
reported octane level. For premium grade, 14 out of 105 samples failed (they didn't meet ASTM specification
and the FTC Octane posting rule). How many samples would be needed to create a 99% confidence interval
that is within 0.02 of the true proportion of premium grade fuel-quality failures?
(14/105)(91/105)(2.5758/0.02)2 =
4148
2838
1913
744
54
23. A state education agency designs and administers high school proficiency exams. Historically, time to
complete the exam was an average of two hours with a standard deviation of 5 minutes. Recently the format
of the exam changed and the claim has been made that the time to complete the exam has changed. A
sample of 50 new exam times yielded an average time of 118 minutes. Calculate a 99% confidence interval
based on the sample result.
Confidence Interval = ( 118 - 2.576(5.000)/sqrt(50) , 118 + 2.576(5.000)/sqrt(50) ) = ( 116.18 , 119.82 )
[117.61 120.09]
[117.36 119.39]
[116.18 119.82]
[115.67 120.33]
[115.82 120.18]
24. The MPG (Miles per Gallon) for a mid-size car is normally distributed with a mean of 32 and a standard
deviation of .8. What is the probability that the MPG for a selected mid-size car would be: More than 33.2?
100P(MPG>33.2) = 100P(Z > (33.2-32)/0.8) =
43.32%
6.68%
93.32%
86.64%
13.36%
25. If we are testing the significance of the independent variable X1 in Regression and we reject the null
hypothesis H0: B1=0, we conclude that:
X is significantly related to Y (should be X1 not X)
X1 is not significantly related to Y
X1 is an unimportant independent variable
B1 is significantly related to the dependent variable Y
26. In a manufacturing process, we are interested in measuring the average length of a certain type of bolt.
Based on a preliminary sample of 9 bolts, the sample standard deviation is .3 inches. How many bolts should
be sampled in order to make us 95% confident that the sample mean bolt length is within .02 inches of the
true mean bolt length?
(1.96(0.3)/0.02)2 =
865
80
1470
3989
1197
27. The changing ecology of the swamps in Louisiana has been the subject of much environmental research.
One water-quality parameter of concern is the total phosphorous level. Suppose that the EPA makes 15
measurements in one area of the swamp, yielding a mean level of total phosphorus of 12.3 parts per billion
(ppb) and a standard deviation of 5.4 ppb. The EPA wants to test whether the data support the conclusion
that the mean level is less than 15 ppb. Calculate the appropriate test statistic to test the hypotheses.
Test Statistic = [ 12.3 - 15 ] / [ 5.4/sqrt(15) ]
7.50
1.94
3.88
-1.94
-7.50
28. If the sampled population has a mean 48 and standard deviation 16, then the mean and the standard
deviation for the sampling distribution of X-bar (sample mean) for n=64
4 and 4
12 and 4
48 and 2
48 and 1/4
48 and 16
29. When we carry out a chi-square test of independence, as the difference between the respective observed
and expected frequencies decrease, the probability of concluding that the row variable is independent of the
column variable
Decreases
Increases
May increase or decrease depending on the number of rows and columns
Will be unaffected
30. The mean life of pair of shoes is 40 months with a standard deviation of 8 months. If the life of the
shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36
months?
1,000,000P(Life < 36) = 1,000,000P(Z < (36-40)/8)
500,000
808,500
191,500
308,500
31. A set of final examination grades in a calculus course was found to be normally distributed with a mean
of 69 and a standard deviation of 8.
Only 5% of the students taking the test scored higher than what grade?
(Show moderate work)
P(Score > x) = 0.05 = P(Z > (x-69)/8)
x = 69+1.64485(8) = 82.2
32. Consider the following partial computer output for a multiple regression model.
Predictor Coefficient Standard Deviation
Constant 41.225 6.380
X1 1.081 1.353
X2 -18.404 4.547
Analysis of Variance
Source DF SS
Regression 2 2270.11
Error 26 3585.75
What is the number of Observations in the sample?
29
Write the least squares regression (prediction) equation.
Y = 41.225 + 1.081X1 - 18.404X2
Test the usefulness of variable x2 in the model at alpha =.05. Calculate the t statistic and state your
conclusions.
Test statistic = -18.404/4.547 = -4.05
t(0.025,26) = -2.056
Conclude X2 is useful at alpha = 0.05.
33. A recent study conducted by the state government attempts to determine whether the voting public
supports further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens.
1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like
to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in
cigarette taxes is significantly greater than .66 at 5% and 10% significance levels. Indicate which test you
are performing;
One-proportion z-test
show the hypotheses,
H0: p ≤ 0.66
Ha: p > 0.66
the test statistic
Test Statistic = ( 0.680 - 0.66 ) / sqrt( 0.66 ( 0.34 )/1500 ) = 1.635
and the critical values
5% critical value = z(0.95) = 1.645
10% critical value = z(0.9) = 1.282
and mention whether one-tailed or two-tailed.
One-tailed
Conclude: Not significantly greater than 0.66 at 5%.
Significantly greater than 0.66 at 10%.
34. (I tried to put all the signs in here… they may not come in properly.. I can maybe send them to you
another way?)
Test H0: pi1 – pi2 <=.01, HA : pi1 – pi2 > .01 at alpha =.05 where p1 =.08, p2 =.035, n1 = 200, n2 =
400.
Indicate which test you are performing;
2-proportion z-test
show the test statistic
Standard error of p difference = sqrt[ 0.08(0.92)/200+0.035(0.965)/400 ] = 0.0213
Test Statistic = ( 0.080 - 0.035 - 0.01) / 0.0213 = 1.643
and the critical values
Critical value = z(0.95) = 1.6449
and mention whether one-tailed or two-tailed.
One-tailed
Conclusion: Do not reject H0.
35. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state.
The amount of juice squeezed from each of these apples is known to be normally distributed with a mean of
2.25 ounces and a standard deviation of 0.15 ounce. Between what two values (in ounces) symmetrically
distributed around the population mean will 80% of the apples fall?
xL = 2.25 - 1.282(0.15) = 2.06
xU = 2.25 + 1.282(0.15) = 2.44
Between 2.06 ounces and 2.44 ounces.
36. The weight of a product is normally distributed with a standard deviation of .5 ounces. What should the
average weight be if the production manager wants no more than 10% of the products to weigh more than
4.8 ounces?
P(X > 4.8) ≤ 0.10
=P(Z > (4.8-average)/0.5) ≤ 0.10
Average ≤ 4.8-1.282(0.5) = 4.16 ounces
37. An insurance company estimates 35 percent of its claims have errors. The insurance company wants to
estimate with 90 percent confidence the proportion of claims with errors. What sample size is needed if they
wish to be within 5 percentage points of the actual?
0.35(0.65)(1.6449/0.05)2 = 247
38. A human resource manager is interested in whether absences occur during the week with equal
frequency. The manager took a random sample of 100 absences and created the following table:
Monday 28
Tuesday 20
Wednesday 12
Thursday 18
Friday 22
At a significance level of alpha = .05 test the Null that the probabilities of absences are the same for all five
days.
2
2
2
2
2
[(28-20) +(20-20) +(12-20) +(18-20) +(22-20) ]/20 = 6.8
2
χ (0.05,4) = 9.488
Conclude the probabilities of absences are equal for all 5 days.
39.
At a recent meeting of educational researchers comparison were made between the type of college freshmen
attend and the numbers who drop out. A random sample of freshmen show the following results: (keep two
decimals in calculating expected frequencies)
4Yr public 4Yr private 2Yr public 2Yr private
drop out 10 9 15 9
don't drop 26 28 18 27
Use a significance level of .05 and determine if the type of school and the drop out rate are independent.
40.
A small town has a population of 15,000 people. Among these 1,500 regularly visit a popular local bar. A
sample of 225 people from those who regularly visit the bar is surveyed for their annual expenditures in the
bar. It is found that on average each person who regularly visits the bar spends about $2000 per year in the
bar with a standard deviation of $196. Construct a 99 percent confidence interval around the mean annual
expenditure in the bar.