# Mathematics

Q19. A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result.

 Did Well on Midterm Did Poorly on Midterm Studying for Exam 80 20 Went Bar Hopping 30 70

Referring to the table, of those who did well on the midterm in the sample, _______ percent of them went bar hopping the weekend before the midterm.

a. 15

b. 27.27

c. 30

d. 50

Q20. Tim was planning for a meeting with his boss to discuss a raise in his annual salary. In preparation, he wanted to use the Consumer Price Index to determine the percentage increase in his salary in terms of real income over the last three years. Which method of data collection was involved when he used the Consumer Price Index?

a. Published sources

b. Experimentation

c. Surveying

d. Observation

Q21. A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below.

 Stem Leaves 3 24 4 3478999 5 112345 6 12566 7 1 8 9 2

Referring to the table, what percentage of the respondents rated overall television quality with a rating between 50 and 75?

a. 0.11

b. 0.40

c. 0.44

d. 0.56

Q22. The process of using sample statistics to draw conclusions about true population parameters is called:

a. statistical inference.

b. the scientific method.

c. sampling.

d. descriptive statistics.

Q23. If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?

a. 0

b. 0.50

c. 1.00

d. Cannot be determined from the information given.

Q24. Which of the following is most likely a parameter as opposed to a statistic?

a. The average score of the first five students completing an assignment.

b. The proportion of females registered to vote in a county.

c. The average height of people randomly selected from a database.

d. The proportion of trucks stopped yesterday that were cited for bad brakes.

Q25. Selection of raffle tickets from a large bowl is an example of:

a. sampling with replacement.

b. sampling without replacement.

c. subjective probability.

d. None of the above.

Q26. The portfolio expected return of two investments

a. will be higher when the covariance is zero.

b. will be higher when the covariance is negative.

c. will be higher when the covariance is positive.

d. does not depend on the covariance.

Q27. Given the numbers: 1, 3, 5, 7, 8 what are the average and the median?

a. Average = 4.8; Median = 5.0

b. Average = 5.0; Median = 5.0

c. Average = 4.8; Median = 4.8

d. Average = 5.0; Median = 4.8

Q28. The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is:

a. 0.10

b. 0.25

c. 0.667

d. 0.733

Q29. A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

a. 0.86466

b. 0.60653

c. 0.39347

d. 0.13534

Q30. The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.

 Time (in Minutes) Relative Frequency 0 but less than 5 0.37 5 but less than 10 0.22 10 but less than 15 0.15 15 but less than 20 0.10 20 but less than 25 0.07 25 but less than 30 0.07 30 or more 0.02

Referring to the table, what is the width of each class?

a. 1 minute

b. 5 minutes

c. 2%

d. 100%

Q31. The probability that

·         house sales will increase in the next 6 months is estimated to be 0.25.

·         the interest rates on housing loans will go up in the same period is estimated to be 0.74

·         house sales or interest rates will go up during the next 6 months is estimated to be 0.89

The probability that house sales will increase but interest rates will not during the next 6 months is:

a. 0.065

b. 0.15

c. 0.51

d. 0.89

Q32. Which of the mean, median, mode, and geometric mean are resistant measures of central tendency?

a. The mean and median.

b. The median and mode.

c. The mode and geometric mean.

d. The mean and mode.

Q33. The probability that

·         house sales will increase in the next 6 months is estimated to be 0.25

·         the interest rates on housing loans will go up in the same period is estimated to be 0.74

·         house sales or interest rates will go up during the next 6 months is estimated to be 0.89

The probability that neither house sales nor interest rates will increase during the next 6 months is:

a. 0.11

b. 0.195

c. 0.89

d. 0.90

Q34. Which of the following statistics is not a measure of central tendency?

a. Mean.

b. Median.

c. Mode.

d. Q3.

Q35. The width of each bar in a histogram corresponds to the:

a. differences between the boundaries of the class.

b. number of observations in each class.

c. midpoint of each class.

d. percentage of observations in each class.

Q36. In left-skewed distributions, which of the following is the correct statement?

a. The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3.

b. The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation.

c. The distance from the smallest observation to Q2 is smaller than the distance from Q2 to the largest observation.

d. The distance from Q1 to Q3 is twice the distance from Q1 to Q2.

Q37. The Central Limit Theorem is important in statistics because:

a. for a largen, it says the population is approximately normal.

b. for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.

c. for a largen, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

d. for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Q38. A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result.

 Did Well on the midterm Did Poorly on Midterm Studying for Exam 80 20 Went Bar Hopping 30 70

Referring to the table, _______ percent of the students in the sample went bar hopping the weekend before the midterm and did well on the midterm.

a. 15

b. 27.27

c. 30

d. 50

Q39. Which of the following statements about the median is not true?

a. It is more affected by extreme values than the mean.

b. It is a measure of central tendency.

c. It is equal to Q2.

d. It is equal to the mode in bell-shaped “normal” distributions.

Q40. A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60?

a. No, and we are 90% sure of it.

b. No. The proportion is 54.17%.

c. Maybe. 0.60 is a believable value of the population proportion based on the information above.

Q1. The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.256 when testing H0: ρ = 0 against the two-sided alternative H1: ρ ≠ 0. To test H0: ρ = 0 against the one-sided alternative H1: ρ > 0 at a significance level of 0.193, the p-value is
a. 0.256/2
b. 0.256
c. 1 – 0.256
d. 1 – 0.256/2

Q2. A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

 Size Mean Std Dev Females 18 48,266.7 13,577.63 Males 12 55,000 11,741.29 Std Error = 4,764.82 Means Diff = -6,733.3 Z = -1.4528 2-tailed p value = 0.1463 T = -1.4221 2-tailed p value = 0.1574

Referring to the table, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?
a. Both populations of salaries (male and female) must have approximate normal distributions.
b. The population variances are approximately equal.
c. The samples were randomly and independently selected.
d. All of the above assumptions were necessary.

Q3. The Y-intercept (b0) represents the:
a. predicted value of Y when X = 0.
b. change in estimated average Y per unit change in X.
c. predicted value of Y.
d. variation around the sample regression line.

Q4. A local real estate appraiser analyzed the sales prices of homes in 2 neighborhoods to the corresponding appraised values of the homes. The goal of the analysis was to compare the distribution of sale-to-appraised ratios from homes in the 2 neighborhoods. Random and independent samples were selected from the 2 neighborhoods from last year’s homes sales, 8 from each of the 2 neighborhoods. Identify the nonparametric method that would be used to analyze the data.
a. the Wilcoxon Signed-Ranks Test, using the test statistic Z
b. the Wilcoxon Signed-Ranks Test, using the test statistic W
c. the Wilcoxon Rank Sum Test, using the test statistic T1
d. the Wilcoxon Rank Sum Test, using the test statistic Z

Q5. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:
a. -4.12
b. -2.33
c. -1.86
d. -0.07

Q6. A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (W, X, Y, and Z). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.

W: 1.2, 1.1, 0.9, 0.4
X: 2.5, 2.1, 1.9, 1.6
Y: 1.0, 1.5, 1.1, 1.3
Z: 0.8, 1.3, 1.1, 0.7

Interpret the results of the analysis summarized in the following table:

 Source df SS MS F PR > F Neighborhoods 2.97 0.990 8.31 0.0260 Error 12 Total 4.40

Referring to the table, the within group mean squares is
a. 0.119
b. 0.990
c. 1.109
d. 8.31

Q7. If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to:
a. autocorrelation.
b. the presence of dummy variables.
c. the absence of dummy variables.
d. collinearity.

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