1. The times required by three workers to perform an assembly-line task were recorded on five
randomly selected occasions. Here are the times, to the nearest minute
Henok
7
11
8
10
10
9
7
Abel
7
8
7
11
9
10
Dawit
11
10
6
7
9
8
10
9
a. Construct the hypothesis
b. Construct the one-way ANOVA table for the data
c. Give us your conclusion
2. A machine is set up such that the average content of juice per bottle equals µ. A sample of 36
bottles yields an average content of 48.5cl. Can you reject the hypothesis that the average
content per bottle is less than or equal to 45cl in favour of the alternative that it exceeds 45cl
(5% significance level)? Assume that the population standard deviation σ = 5cl.
3. Interest is focused on whether the repeal of the national maximum speed limit had an effect on
the mean speeds on Indiana roads. To test this hypothesis, 744 observations in the before
period and 552 observations in the after the repeal period are used. A 5% significance level is
used. Descriptive statistics show that average speeds in the before and after periods are 57.65
and 60.48, respectively. Further, the variances for before and after the repeal periods are 16.4
and 19.1, respectively.
4. There was a probability of 0.8 of success in any attempt to make a telephone call. Calculate the
probability of having 7 successes in 10 trials.
5. Patients arrive at a hospital accident and emergency department at random at a rate of 6 per
hour. Find the probability that during any 90 minute period, the number of Patients at the
hospital accident and emergency department is i) exactly 7 ii) at least 10
6.
Suppose that the number of babies born a month at a hospital follows a Poisson distribution
with a mean of 6.3. a) Find the probability that the next two months will both result in 5 births
each occurring at this hospital. b) Find the probability that at least 2 births occur at this hospital
during a particular one month period. c. calculate the variance
7. Researchers have sought to examine the effects of various types of music on agitation levels in
patients who are in the early and middle stages of Alzheimer’s disease. Patients were selected
to participate in the study based on their stage of Alzheimer’s disease. Three forms of music
were tested: Easy listening, Mozart, and piano interludes. While listening to music, agitation
levels were recorded for the patients based on heart rate in beats per minute. Scores are
recorded below.
Group
Early Stage
Alzheimer’s
Middle Satge
Alzheimer’s
Piano Interlude
103.5
104.7
100.2
105.9
Mozart
69.9
78.5
88.2
73.4
Easy Listening
95.6
99.3
101.4
120.1
Mean: 103.6
99.7
100.5
110.1
115.1
Mean =77.5
70.8
80.9
75.6
90.2
Mean=104.1
119.5
116.4
98.6
96.5
Mean 106.4
Mean=79.4
Mean : 107.8
a. Propose null hypotheses to test whether types of music or stage of Alzheimer’s have
an effect on agitation level.
b. Using the various equations for calculating a two-way ANOVA, explain how to
calculate the values in each box of the following ANOVA table.
Source
Sum of Sq. Degrees of
Mean
F-statistics
P-value
Freedom
square
Type of
music
Degree of
Alzheimer’s
Alzheimer’s
X Music
type
Within
X
X
total
X
X
X
c. Now that you have all the necessary components, using your F-statistic values that
you calculated above, an appropriate α value, and the correct degrees of freedom,
look up the p-values for each category.
d.
Interpret your F-statistic and P-values. Are there any significant main effects or an
interaction effect? 5. Now that you have all the information you need, come up with
a conclusion statement and discuss the relationship between the factors.
8. A transit planning agency wants to estimate at a 95% confidence level,, the share of transit
users in the daily commute market (i.e the percentage of commuters using transit). A random
sample of 100 commuters is obtained and it is found that 28 people in the sample are transit
users. Calculate the confidence interval of transit’s share in the daily commute.
Good luck
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