STATISTICS 2023
NAME IN PRINT__________________________________
FINAL EXAM
SIGNATURE IN INK_______________________________
SPRING 2009
CWID IN INK_____________________________________
FILL IN THE BLANK. Write the word or phrase from the list on the right that belongs in the blank. The
words or phrases in this list may be used more than once or not at all.
(Each blank 3 points each)
1. Confidence intervals are often constructed by adding and subtracting the
___________________________________ from the point estimate for the
parameter.
2 A population _________________________________ is estimated with
sample statistic that is used as point estimator.
3. A point estimate is not equal to the value of the parameter estimated so the
_______________________________________ that is associated with the
point estimator must always be considered.
4. A conclusion about a population based on observed data from a random
sample is called a ______________________________________________ .
5. The statement assumed true and tested for validity in a hypothesis
Standard error
Test statistic
Null hypothesis
Alternative hypothesis
Parameter
Sample statistic
Confidence interval
Point estimate
Bound of error
Population
Sample statistics
Statistical inference
Alpha value
P-value
Rejection region
Critical value
test is the _____________________________________________________ .
6. In a hypothesis test, the probability of observing data at least as extreme as
the data observed is the ________________________________________________ of the test.
7. The statement that can be supported by data in a hypothesis test is the
_____________________________________________________ .
8. When the null hypothesis is rejected based on certain data then the probability of error when
the rejection decision is made is called the __________________________________ of the test.
9. A single number, which is a measure of relative standing, that is calculated from the data on which the
validity of the null hypothesis is evaluated is called the ________________________________________ .
10. The _____________________________________ divides the distribution of the test statistic
under a true null hypothesis into likely and unlikely values of the test statistic.
STATISTICS 2023
FINAL EXAM
SPRING 2009
STATE THE ANSWER. Write the answer on the line.
PAGE TWO
(3 points each)
___________________11. What is the P(Z< -.85) + P(Z>.52)?
___________________12. The number of stock trades in a random sample of 8 days is 346,
645, 435, 745, 867, 456, 851, and 879. What is the numerical value of the point estimate for
the population mean number of stock trades per day based on this sample?
___________________13. The number of stock trades in a random sample of 8 days is 346,
645, 435, 745, 867, 456, 851, and 879. What is the numerical value of the point estimate for
the population standard deviation of the number of stock trades per day based on this sample?
Round your answer to two digits past the decimal.
___________________14. If a hypothesis test based on a large sample has a test statistic
value of 0.75 and the researcher is trying to prove that the population mean is not equal to
some stated value, what is the p-value of the hypothesis test?
__________________ 15. If the p-value in a two tailed hypothesis test based on a z-test
statistic is equal to 0.2542, what is the magnitude of the test statistic?
___________________16. In a right-tail hypothesis test based on a small sample of 14
observations the value of the test statistic must exceed what number for the researcher to
reject the null hypothesis with only a 0.025 alpha value?
___________________17. If a researcher who is comparing the means of two populations is
attempting to prove that the mean of population two is more than 70 units larger than the mean
of population one what is the appropriate alternative hypothesis?
___________________18. Based on a sample of 18 observations the mean daily decline of a
certain stock is 21.25 units; based on a sample of 16 observations the mean daily decline of a
second stock is 14.45 units. What the is the numerical value of the point estimate for the
difference between the mean daily change for these two stocks based on these two samples?
___________________19. If two samples of the same size produced variance estimates of
543 and 235, what is the numerical value of the pooled variance estimate based on these two
samples?
___________________ 20. If a 95% confidence interval to estimate the difference between
two population means is (-34.56, -56.22) then the hypothesis of equal population means would
be rejected at the 5% alpha significance level? Answer: yes, no, maybe, or can’t tell.
STATISTICS 2023
FINAL EXAM
SPRING 2009
PAGE THREE
STATE THE ANSWER. Write the answer on the line.
(3 points each)
Two types of accounting software were being compared in terms of the mean number of
account audits that each type could complete in a set time period. For each type of software
the number of account audits performed in a set time period was recorded for each of 100 time
periods. The sample statistics for the numbers of account audits per time period for each type
of accounting software are as follows.
Software One
n1=100
mean=7086
variance=1764
Software Two
n2=100
mean=8763
variance=2704
___________________21. What is the estimated standard error of the point estimate for the
mean number of audits per time period for the first type of accounting software?
___________________22. What is the numerical value of the point estimate for the difference
between the mean number of audits per time period for the two types of accounting software?
___________________23. What is the estimated standard error of the point estimate for the
difference between the mean number of audits per time period for the two types of accounting
software, if the population variances are not assumed equal?
___________________24. If the estimated standard error of the point estimate for the
difference between the mean number of audits per time period for the two types of accounting
software is 7 units what is the bound of error for a 95% confidence interval to estimate the
difference between the mean number of audits per time period for the two types?
___________________25. A pooled variance estimate would probably not be used in this
case due to not assuming equal variances, but if it were calculated what would be the
numerical value of the pooled variance estimate based on these two samples?
___________________26. The observed test statistic in this case would have to exceed what
magnitude for the data to indicate at the 1% significance level that the two types of accounting
software do not result in equal mean number of audits in a set time period?
STATISTICS 2023
FINAL EXAM
SPRING 2009
PAGE FOUR
LINEAR REGRESSION QUESTIONS. Write the answer on the line.
(3 point each)
The number of classes missed by students is used to predict their final grade. The bivariate
data recorded below are number of classes missed (X) and class grade (Y). Five students
were randomly sampled and the number of classes missed and their final grade in the class
were recorded. Use this data to answer the following questions.
X
Y
1
99.5
2
80.5
3
62.2
5
50.1
8
39.8
__________________27. What is the numerical value of the corrected sum of squares for the
y-variable based on the above data?
__________________28. What is the least squares estimate of the slope in the linear
regression equation to estimate the class grade from the number of classes missed? Round
your answer to three digit past the decimal.
__________________29. What is the least squares estimate of the y-intercept in the linear
regression equation to estimate the class grade from the number of classes missed? Round
your answer to one digit past the decimal.
________________________________30. Write the estimated regression equation to
estimate the class grade from the number of classes missed. Use the estimates of the slope
and y-intercept that you calculated in problems 28 and 29 above.
__________________31. What is the numerical value of the estimated linear correlation
between the two variables? Round your answer to three digits past the decimal.
ANOTHER LINEAR REGRESSION QUESTION.
The estimated linear regression equation below uses X=electricity cost to estimate Y=total
manufacturing cost of a certain product. Use it to answer the remainder of the questions on
this page.
^
y = 1,504 + 19.2x
__________________32. When the electricity cost is $485 what is the least squares estimate
for the total manufacturing cost of the product?
__________________33. If the estimated standard error for the estimate of the slope is 6.4
what is the value of the test statistic to test whether the slope is equal to zero?