(Multiple Choice Questions)
(30
marks, 1 Mark Each)
1.
An assumption made about the value of a population parameter is called a
a.
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hypothesis
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b.
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conclusion
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c.
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confidence
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d.
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Significance
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2.
In hypothesis testing, the tentative assumption about the population parameter is
a.
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the alternative hypothesis.
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b.
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the null hypothesis.
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c.
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either the null or the alternative.
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d.
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None of these alternatives is correct.
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3.
What type of error occurs if you fail to reject H0
when, in fact, it is not true?
a.
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Type II
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b.
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Type I
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c.
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either Type I or Type II, depending on the level of significance
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d.
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either Type I or Type II, depending on whether the test is one tail or two tail
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4.
The
p-value
a.
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is the same as the Z statistic.
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b.
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measures the number of standard deviations from the mean.
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c.
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is a distance.
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d.
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is a probability.
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5.
In hypothesis testing if the null hypothesis is rejected,
a.
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no conclusions can be drawn from the test.
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b.
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the alternative hypothesis is true.
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c.
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the data must have been accumulated incorrectly.
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d.
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the sample size has been too small.
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6.
The level of significance
a.
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can be any positive value.
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b.
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can be any value.
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c.
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is (1 - confidence level).
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d.
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can be any value between -1.96 to 1.96 .
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7.
TheA hypothesis test for a population proportionp
is given below:
H
0:p
= 0.10
H
a:p
? 0.10
Sample sizen
= 100 and sample proportion = 0.15.z-statistic = ?
a.
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1.67
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b.
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0.04
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c.
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1.12
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d.
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-1.12
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8.
The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are
a.
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H0: m³ 700 Ha: m
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b.
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H0: m = 700 Ha: m¹ 700
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c.
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H0: m> 700 Ha: m£700
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d.
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H0: m
a: m³ 700
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9.
A student believes that the average grade on the final examination in statistics is at least 85. She/He plans on taking a sample to test her belief. The correct set of hypotheses is
a.
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H0:m
a: m 85
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b.
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H0:m 85 Ha: m > 85
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c.
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H0:m 85 Ha: m
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d.
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H0:m > 85 Ha: m 85
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10.
The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is
a.
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H0:m
a: m 5
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b.
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H0:m 5 Ha: m > 5
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c.
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H0:m > 5 Ha: m 5
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d.
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H0:m 5 Ha: m
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11.
A null hypothesis is that the mean height of men and women are the same. The alternative hypothesis is that men have a longer mean height than women. Which of the following is the correct way to state the null hypothesis?
a.
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H0: p= 0.50
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b.
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c.
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H0: p1– p2
= 0
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d.
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H0:m1 -m2= 0
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12.
Refer to Q11. A statistical test is performed for assessing if men have a longer mean height than women. Thep-value is 0.225. Which of the following is the most appropriate way to state the conclusion?
a.
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The mean height of the populations of men and women are identical.
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b.
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There is not enough evidence to say that that the populations of men and women have different mean height.
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c.
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Men have a greater mean height than women.
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d.
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The probability is 0.225 that men and women have the same mean height.
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13.
Sample sizes n1
= 100, n2
= 100 and numbers x1
= 39, x2
= 41 of successes to find the pooled estimate .
a.
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0.360
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b.
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0.400
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c.
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0.800
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d.
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0.450
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14.
If the regression equation is = 2 – 0.4X, what is the value of when
X= –3?
15.
Which of the following can not
be answered from a regression equation?
a. Predict the value of
yat a particular value of
x.
b. Estimate the slope between
y
and
x.
c. Estimate whether the linear association is positive or negative.
d. Estimate whether the association is linear or non-linear
16.The equation of a regression line is called the regression equation.
a. True
b. False
17.The regression line for a set of points is given by = 12-6x.
What is the slope of the line?
18.If the correlation coefficient between X and Y is one, then there is no linear
Correlation.
a. True
b. False
19.Two samples are independent if the sample values from one population are not related to or somehow naturally paired or matched with the sample values from the other population.
a. True
b. False
20.A two-tailed test is one where:
a. results in only one direction can lead to rejection of the null hypothesis
b. negative sample means lead to rejection of the null hypothesis
c. results in either of two directions can lead to rejection of the null hypothesis
d. no results lead to the rejection of the null hypothesis
21. The chi-square goodness-of-fit test can be used to test for:
a. significance of sample statistics
b. difference between population means
c. normality
d. probability
22.The ANOVA test is based on which assumptions?
I. the sample are randomly selected
II. the population variances are all equal to some common variance
III. the populations are normally distributed
IV. the populations are statistically significant
a. All of the above
b. II and III only
c. I, II, and III only
d. I, and III only
23.
The chi-square test can be too sensitive if the sample is:
a. very small
b. very large
c. homogeneous
d. predictable
24.
One-way ANOVA is used when:
a. analyzing the difference between more than two population means
b. analyzing the results of a two-tailed test
c. analyzing the results from a large sample
d. analyzing the difference between two population means
25.Typically one-way ANOVA is used in which of the following situations?
I. there are several distinct populations
II. there are two sample populations over 4000
III. randomized experiments
IV. randomly selected populations
a. All of the above
b. II and III only
c. I, II, and III only
d. I, and III only
26.The chi-square test is not very effective if the sample is:
a. small
b. large
c. irregular
d. heterogeneous
27.In a one-way analysis of variance, the “Sum of Squared Errors” is a measure of the
a. variation among population means
b. variation among individuals within groups
c. variation among observed sample means
d. variation among sample sizes
28.
When a one-way analysis of variance test is done, what probability distribution is used to find the p-value?
a. F-distribution
b. normal distribution
c. Chi-square distribution
d. t-distribution
29.
Ifm1,m2
andm3
are the population means of GPA for the about right, overweight and underweight groups, respectively, then the alternative hypotheses tested by ANOVA:
a. m1,m2
andm3
are all different.
b. At least two ofm1,m2
andm3
are different from each other.
c. m1
=m2¹m3
d. m1
>m2
>m3
30.A one-way analysis of variance will be done to compare systolic blood pressures in three different age groups. What is the correct statement of the null hypothesis?
a. m1=m2=m3
b. m1¹m2¹m3
c. = =
d.
¹ ¹
Q.
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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15
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A.
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Q.
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16
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17
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18
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19
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20
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21
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22
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23
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24
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25
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26
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27
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28
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29
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30
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A.
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Section –II
Answer the following Short Type Questions
(12 marks, 2 Mark Each)
1. Assumethat a simple random sample has been selected from a normally distributed population. Test the claim that the mean age of the prison population in one city is less than 26 years. Sample data are summarized as n = 25, = 24.4 years, and s = 9.2 years. Use a significance level ofa = 0.05, p-value = 0.1966, critical value : t = -1.711
2.
For the Salary _ Experience data set, test to see if there is a difference in salaries for employees who selection into their current position was from within the company (internal employees) versus who were selected into their position from outside the company (external employees).
The XL output is as follows. Comparing Salaries (x$1000)
t-test : two-sample Assuming non-equal variances
Continuous…………..
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External salary A
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Internal salary B
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mean
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78.35
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66.90
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variance
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87.94
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79.68
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observations
|
62
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88
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Pooled variance
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83.08
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Hypothesized Mean Difference
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0
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df
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148
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T stat
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7.581
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P(T
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0.000
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t-critical one -tail
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1.655
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P(T
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0.000
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t-critical one -tail
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1.975
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a. State the null hypotheses and alternative hypotheses.
b. What is test statistics give answer with formula.
c. Conclusion?
3. A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The standard deviation of the
population
(s) is known to be 5.6 days.
a.
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Using the critical value approach, test to determine if their advertisement is legitimate. Leta = .05.
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b.
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Using the
p-value approach, test the hypotheses at the 5% level of significance.
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4. A company wants to study the relationship between an employee's length of employment and their number of workdays absent. The company collected the following information on a random sample of seven employees.
Number of Workdays Absent
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2
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3
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3
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5
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7
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7
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8
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Length of Employment (in yrs)
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5
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6
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9
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4
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2
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2
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0
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Q1. What is the slope of the linear equation?
Q2. What is the Y intercept of the linear equation?
5. Students at multiple grade schools were asked what their personal goal ( grades, be good and bad at sports) was and what good grades and bad grades were. The data is in table ("Popular kids data file," 2013). Calculate the Chi-square test.
Table: Personal Goal and Importance of Grades
Goal
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Grades Importance Rating
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Row Total
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Good
|
Bad
|
Grades
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70
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66
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136
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Sports
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10
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24
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34
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Column Total
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80
|
90
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170
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6. While conducting a one-way ANOVA comparing five treatments with 10 observations per treatment, you compute SST = 250 and MSE = 3. Construct ANOVA table and find the value of F?
Section –III
Answer the following Long Type Questions
(18 marks, 3 Mark Each)
1. Tata- Corporation is a company has a stable workforce with little turnover. They have been in business for 50 years. It has more than 10,000 employees.
The company has always promoted the idea that its employees stay with them for a very long time, and it has used the following line in itsrecruitment brochures: "The average tenure of our employees is 20 years."
Since Tata-corporation isn't quite sure if that statement is still true, a random sample of 100 employees is taken and the average age turns out to be 19 years with a standard deviation of 4 years. Can Tata continue to make its claim, or does it need to make a change?
a. State the hypotheses.
b. What is the test statistic? (Note that the sample is randomly selected from a population that is assumed to be normally distributed and/or we have a large sample)
c. Specify thesignificance level
d. Calculations: The calculated z value is -2.5
It has p = 0.0062
Reject or fail to reject the null?
e. Conclusion?
f. What type of the error?
2. An airport official wants to assess if the flights from one airline (Airline 1) areless delayed
than flights from another airline (Airline 2). Let = average delay for Airline 1 and = average delay for Airline 2. A random sample of 10 flights for Airline 1 shows an average of 9.5 minutes delay with a standard deviation of 3 minutes. A random sample of 10 flights for Airline 2 shows an average of 12.63 minutes delay with a standard deviation of 3 minutes. Assume delay times are normally distributed, but do not assume the population variances are equal. Use the conservative “by hand” estimate for the degrees of freedom.
p-value = 0.022
a. What are the appropriate null and alternative hypotheses?
b. What is the value of the test statistic?
c. For a significance level ofa
= 0.05, are the results statistically significant?
d. Which of the following is an appropriate conclusion?
3. Assume you send your salespeople to a “customer service” training workshop. Has the training made a difference in the number of complaints? What is hypotheses? Calculate test statistics and give conclusion. You collect the following data. (Test at the 0.01 level).
4. Find Linear correlation coefficient between X and Y for the following data:
Hours X
|
1
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1
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3
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4
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6
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7
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8
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8
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Score Y
|
1
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3
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2
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5
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4
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5
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7
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8
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5. Suppose a die throw, check it is fair or not. If it is fair then the proportion for each value should be the same. It is need to find the observed frequencies and to accomplish this roll the die 500 times and count how often each side comes up. The data is in table. Do the data show that the die is fair? Test at the 5% level.c2
cdf(5)˜0.913
Table: Observed Frequencies of Die
Die values
|
1
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2
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3
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4
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5
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6
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Total
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Observed Frequency
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78
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87
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87
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76
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85
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87
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100
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1. State the null and alternative hypotheses and the level of significance
2.
Find thec2
-test.
3.Conclusion?
6. While conducting a one-way ANOVA comparing three salary/experience group
Use the Salary/Experience data set. At the 0.05 significance level, is there a difference in mean salary among the experience groups of the employees?
High Level Experience: employees with 10 or more years of experience in the field
Moderate Experience: employees with 6 to 9 years of experience in the field
Low Experience: employees with 5 or less years of experience in the field
with following observation in table,
give appropriate hypotheses. Construct ANOVA table and find the value of F and conclusion? Fcrt
= 3.0576 , p-value = 0.00005
salary by experience
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summary
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Group
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count
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sum
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average
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variance
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H EXP Sal
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48
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3255
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67.8
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84.9
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H EXP Sal
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57
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4059
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71.2
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111.7
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H EXP Sal
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45
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3431
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76.2
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117.2
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