STAT 3321 – Final, Spring, 2007 – Green Exam - Printed Name______
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Directions
1. Do not open exam until told.
2. Bubble in your last name, skip a space, and then your first name on the scantron.
3. Set all pagers and cell phones to silent and place on floor or backpack
4. When finished place your printed material inside your exam and place on desk in front.
5. Check the board for corrections to the exam before leaving.
6. You can not use your phone as a calculator.
7. Assume a = 0.05 and 95% confidence unless told otherwise.
I have read and I understand all the directions above.
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Signature
1 Suppose P(A) = 0.35. The probability of the complement of A is:
a. 0.35
b. 0.65
c. 0.50
d. 0.35
e. 0.05
2 If P(A) = 0.35, P(B) = 0.45 and P(A and B) = 0.25, then P(A|B) is:
a. 0.714
b. 0.556
c. 1.4
d. 1.8
e. 0.45/0.35
3 You are trying to predict the starting salary of students based on their GPA. You find a 95% the population intercept is 25,000 with a margin of error of ±2,000 . Which of the following is a correct interpretation of the interval values? With 95% confidence we can say that ….
a. for each one point increase in GPA, the average starting salary is 25,000 with a margin of error of ±2,000.
b. I haven't the foggiest idea what this means. (This might be true, but this answer will still be counted wrong.)
c. when the starting salary is zero, a student’s GPA will be between $25,000.
d. when GPA is zero, the average starting salary increases by 25,000 with a margin of error of ±2,000.
e. when GPA is zero, the average starting salary is 25,000 with a margin of error of ±2,000.
4 Which of the following is true about the sampling distribution of the sample mean?
a. The shape of the sampling distribution is always normal even for small sample sizes.
b. The standard deviation of the sampling distribution is always equal to the population standard deviation.
c. The sampling distribution is a list of all possible sample sizes.
d. All of these are true.
e. The mean of the sampling distribution is always equal to the population mean .
5 When trying to estimate the population mean, the typical error in the sample mean is also called the:
a. standard error of the mean.
b. finite population correction factor.
c. central limit theorem.
d. population standard deviation.
e. margin of error
6 Which of the following would be an appropriate alternative hypothesis?
a. The mean of a population is equal to 70.
b. The mean of a sample is greater than 55
c. The mean of a sample is equal to 55.
d. The mean of a population is greater than 70..
e. the sample standard deviation is > 3
7 The expected number of heads in 100 tosses of an unbiased coin is:
a. 100
b. 25
c. 75
d. 50
e. 75
8 A 98% confidence interval estimate for a population mean is determined to be 75.38 to 86.52. If the confidence level is reduced to 90%, the confidence interval:
a. becomes narrower.
b. increases its confidence
c. remains the same.
d. becomes wider.
e. None of these choices.
9 Which of the following measures can be used with both numerical and categorical variables?
a. the mode
b. the median
c. the arithmetic mean
d. the standard deviation
e. the scatter plot
10 Researchers determine that 60 Kleenex tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: x= 52 and s = 22. Using the sample information provided, what is the value of the test statistic?:
a. t = (52 - 60)/(22/100)
b. t = (52 - 60)/(22/10)
c. t = (52 - 60)/22
d. t = (52 - 60)/(22/1002 )
e. none of the above
11 A normally distributed population has a mean of 60 and a standard deviation of 10. You obtain a random sample of size 25.The probability that the sample mean will be smaller than 56 is:
a. 0.0166
b. 0.0394
c. 0.3708
d. 0.0228
e. none of the above
12 In performing a regression analysis involving two numerical variables, we are assuming:
a. All of these choices are correct.
b. the variances of x and y are equal.
c. y has the same variation for each x value..
d. that x and y are independent.
e. the distribution of x is normal.
13 The classification of student major (accounting, economics, management, marketing, other) is an example of:
a. a categorical or qualitative random variable.
b. a discrete random variable.
c. a continuous random variable.
d. a parameter.
e. a scatter plot
14 In the simple linear regression model, the slope represents the:
a. average change in x per unit change in y
b. value of y when x = 0
c. value of x when y = 0..
d. average change in y per unit change in x..
e. the value of y given a value of x.
15 In testing the hypotheses: H0 : vs. H1:≠ , the following statistics are available: n = 10, b = 1.8, b = 2.45, and Sb1= 1.20. The value of the test statistic is:
a. 1.50
b. 0.300
c. 1.96
d. 0.306
e. 2.042
16 Which of the following is not a measure of central tendency?
a. the standard deviation
b. the mode
c. the mean
d. the median
e. all of the others are measures of central tendency
17 In regression analysis, the coefficient of determination R2 measures the amount of variation in y that is:
a. caused by the variation in x.
b. associated with the variation in x.
c. the average.
d. unexplained by the variation in x.
e. explained when x=0
18 The hypotheses are H0: = 800 vs. H1:≠ 800. If the value of the Z test statistic equals 1.75, then the p value is:
a. 0.0802
b. 0.0401
c. 0.4599
d. 0.9198
e. 0.05
19 In the past a university has determined that 50% of students receive some sort of financial aid. Assume the proportion of all students receiving financial aid has not changed. In a random sample of size 100, what is the chance of finding at least 55 that receive some sort of financial aid?
a. 0.0228
b. 0.9900
c. 0.1587
d. 0.3459
e. none of the above
20 If we do not reject the null hypothesis, we conclude that:
a. there is enough statistical evidence to infer that the alternative hypothesis is true.
b. the test has made a type II error.
c. there is enough statistical evidence to infer that the null hypothesis is true.
d. there is not enough evidence to infer that the alternative hypothesis is true.
e. it should be rejected
21 Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?
a. A non normal population with a large sample and an unknown population variance.
b. A normal population with a large sample and a known population variance.
c. Non normal population with a small sample and an unknown population variance.
d. A normal population with a small sample and an unknown population variance.
e. A normal population with a small sample size and a known population variance.
22 With 95% confidence, what is the margin of error when estimating a population mean when n= 200, and = 0.4?
a. 0.1535
b. 0.0554
c. 0.2465
d. 0.2554
e. none of the above
23 If Z is a standard normal random variable, then Pr( 1.34 < Z < 1.84) is:
a. 0.0572
b. 0.1056
c. 0.0401
d. 0.8543
e. none of the above
24 Suppose in a sample you find that 25% of the variation of exam 1 scores is associated with variation in the number of hours studied. What statistical term is being interpreted here?
a. The coefficient of determination, R2 .
b. The intercept, b0
c. the t test value, t
d. The standard error of the slope, Sb1
e. the average value of y given x: y|x
25 In simple linear regression, most often we perform a two tail test of the population slope to determine whether there is sufficient evidence to infer that a linear relationship exists. The null hypothesis is stated as:
a. H0 : b1 = 0
b. H0 : 1 = 0
c. H0 : = 0
d. H0 : 1 ≠ 0
e. H0 : 1 > 0
26 It is desired to estimate the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and 95% confidence interval was calculated to be from $2,190,000 to $4,720,000. Based on the interval above, do you believe the average total compensation of CEOs in the service industry is more than $1,000,000?
a. I can conclude that the average exceeds $1,000,000 at the 95% confidence level.
b. No, and I am 95% confident of it.
c. Yes, and I am 80% confident it is less than $1,000,000.
d. I am 95% confident that the average compensation is $1,000,000.
e. The sample size is too small to make a decision.
27 The sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is:
a. 107
b. 8
c. 30
d. 61
e. none of the above
28 The width of a confidence interval estimate of the population mean widens when the:
a. sample size decreases.
b. sample mean decreases
c. level of confidence decreases.
d. value of the population standard deviation decreases..
e. moon is in the seventh house and Jupiter aligns with Mars
29 A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample standard deviation of 5. The upper value (the sample mean plus its margin of error) of a 95% confidence interval for the population mean would equal:
a. 77.273
b. 77.769
c. 72.727
d. 72.231
e. none of the above
30 A multiple choice test has 33 questions. There are 5 choices for each question. A student who has not studied for the test decides to answer all questions randomly. Which of the following distributions can be used to determine his chance of getting at least 20 questions right?
a. hypergeometric distribution
b. binomial distribution
c. Poisson distribution
d. F distribution
e. t distribution
31 The Central Limit Theorem states that, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean:
a. is approximately normal if n < 30.
b. has the same variance as the population.
c. is approximately normal for a sufficiently large sample.
d. is approximately non-normal even if the underlying population is normal.
e. is a hypergeometric distribution
32 Which of the following statements is not true?
a. The height of each rectangle in a bar chart represents the frequency for a particular category.
b. A bar chart is created by drawing a slice of a circle representing each category.
c. Bar charts focus the attention on the frequency of the occurrences of the categories.
d. Bar charts are used with qualitative data.
e. all of the above are correct.
33 When using a sample statistic to estimate a population mean based on continuous data, what do we know?
a. the distribution of the statistic is normal
b. the statistic is close to the population parameter
c. the variability of the statistic is large.
d. The statistic is always in error.
e. the margin of error is the same as the standard deviation
Answers
1b
2b
3e
4e
5a
6d
7d
8a
9a
10b
11d
12c
13a
14d
15e
16a
17b
18a
19c
20d
21c
22b
23a
24a
25B
26a
27e
28a
29b
30b
31C
32b
33d