See attached file for graphs.
1) if the null hypothesis is not rejected, it can be assumed the proportions are __________ and the differences in them are due to chance.
2) A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and for men. At a= .05, what is the test value?
Sample size 50 80
Mean effect 7 6.95
Sample variance 3 4
3) For the samples summarized below, test the hypothesis at =.05 that the two variances are equal.
Variance Number of data values
Sample 1 25 9
Sample 2 9 19
a) Do not reject the hypothesis because the test value 7.72 is greater than the critical value 3.01.
b) Reject the hypothesis because the test value 2.78 is less than the critical value 2.88.
c) Reject the hypothesis because the test value 7.72 is greater than the critical value 2.88.
d) Do not reject the hypothesis because the test value 2.78 is less than the critical value 3.01.
4) A random group of students was selected from a large student conference to analyze their class in school. Is there evidence to reject the hypothesis that the number of students is equally distributed between the four classes, at alpha = .05?
Freshman Sophomore Junior Senior
Number of students 9 9 13 21
a) There is evidence to reject the claim that students are equally distributed between the four classes because the test value 7.815 > 7.385
b) There is not evidence to reject the claim that the customers' preferences are distributed between the four classes because the test value 7.385 < 9.488
c) There is evidence to reject the claim that students are equally distributed between the four classes because the test value 9.488 > 7.385
d) There is not evidence to reject the claim that students are equally distributed between the four classes because the test value 7.385 < 7.815
5) If there are 3 means to be compared, then how many possible different comparisons are there altogether?
6) A marketing firm asked a random set of married and single men as to how much they were willing to spend for a vacation. At alpha = .05, is a difference in the two amounts?
Married men Single men
Sample size 50 50
Mean spending 380 325
Sample variance 6000 9000
a) No, because the test value 0.18 is inside the interval (-1.96, 1.96)
b) Yes, because the test value 3.18 is outside the interval (-1.96, 1.96)
c) Yes, because the test value 1.50 is inside the interval (-1.96, 1.96)
d) No, because the test value 1.50 is outside the interval (-1.96, 1.96)
7) In an Analysis of Variance Summary Table, if the Mean Square Between = 35 and the Mean Square Within = 28, then the null hypothesis of the groups having the same mean is
a) There is not evidence to reject the claim because 35 > 28
b) There is evidence to reject the claim because 35 > 28
c) Cannot be determined without knowing the Sums of Squares (between and within)
d) Cannot be determined without knowing the Degrees of Freedom (between and within)
8) An anatomy teacher hypothesizes that the final grades in her class are distributed as 10% A's, 23% B's, 45% C's, 14% D's, and 8% F's. What is the critical value if at the end of the semester she has the following grades? Use a=0.05.
A B C D F
6 14 22 8 4
9) If the test value in the figure below, for a test of the difference between two large sample means, is 2.57 when the critical value is 1.96, what decision about the hypothesis should be made?
a) reject the null hypothesis
b) do not reject the null hypothesis
c) reject the alternative hypothesis
d) not enough information
10) A researcher wanted to investigate whether there is a significant difference in the average age of instructors, assistant professors, associate professors, and full professors at a university. The faculty was selected at random and their ages were recorded. Use the collected data to complete the ANOVA chart given below.
Instructors assistant professors associate professors professors
26 28 45 58
32 32 48 56
29 36 52 62
36 45 54 65
40 50 62 52
45 46 65 49
source of variation sum of squares degrees of freedom variation F value F critical
between groups 3 12.88 3.10
within groups 1120.17
total 3283.63 23
11) Use the given contingency table to (a) find the expected frequencies of each cell in the table, (b) perform a chi-square test for independence, and (c) comment on the relationship between the two variables. Assume the variables are independent.
The contingency table shows the results of a random sample of 500 individuals classified by gender and type of vehicle owned. Use α = 0.01.
Type of vehicle owned
Gender car truck suv van
Male 90 100 50 7
Female 110 75 65 3
12) Which of the following time-series forecasting methods would not be used to forecast a time series that exhibits a linear trend with no seasonal or cyclical patterns?
a) Dummy variable regression
b) Linear trend regression
c) Holt Winter's double exponential smoothing
d) Multiplicative Winter's method
e) Both A and D
13) In the Durbin-Watson test, if the calculated d-statistic is greater than the upper value of the d-statistic, then
a) We do not reject H0 which says the error terms are not autocorrelated
b) We do reject H0 which says the error terms are not autocorrelated
c) The test is inconclusive
d) We do reject H0, which says the error terms are positively or negatively autocorrelated
14) The demand for a product for the last six years has been 15, 15, 17, 18, 20, and 19. The manager wants to predict the demand for this time series using the following simple linear trend equation: trt = 12 + 2t. What are the forecast errors for the 5th and 6th years?
a) 0, -3
b) 0, +3
c) +2, +5
d) -2, -5
15) The ________ component of a time series measures the fluctuations in a time series due to economic conditions of prosperity and recession with duration of approximately 2 years or longer.
16) If the errors produced by a forecasting method for 3 observations are +3, +3 and -3, then what is the mean absolute deviation?
17) In the multiplicative decomposition method, the centered moving averages provide an estimate of:
a) Trend x seasonal
b) Trend x cycle
c) Seasonal x cycle
d) Trend x irregular
18) Those fluctuations that are associated with climate, holidays and related activities are referred to as__________ variations.
19) Since the ____________ index employs the base period quantities in all succeeding periods, it allows for ready comparisons for identical quantities of goods purchased between the base period and all succeeding periods.
20) When the moving average method is used to estimate the seasonal factors with quarterly sales data, a ______ period moving average is used.
21) When a forecaster uses the _________________ method she or he assumes that the time series components are changing quickly over time.
a) Time series regression
b) Simple exponential smoothing
c) Box and Jenkins method
d) Multiplicative decomposition method
22) The linear trend equation for the following data is ŷ= 1.4286+2.5(t)
Month Value of Fund
a. What is the predicted value of the fund in the period t=1?
b. What is the predicted value of the fund in the period 3, and period 7?
c. Find the residual values (error) for period 3, and period 7.
23) Use the following to answer the questions:
Week Revenue Forecasted Revenue
1 200 225
2 240 220
3 300 285
4 270 290
5 230 250
6 260 240
7 210 250
8 275 240
a. Compute the total error (sum of the error terms).
b. Compute the mean squared error (deviation).
The solution provides answers to multiple choice questions on hypothesis testing and Time series Analysis.