## Transcribed Text

Problem 1. Suppose we are given two independent random samples of sizes n and from
Bernoulli populations with parameters P1 and P2- Let P1 and P2 be the corresponding sample
proportions. Consider the problem of testing the hypotheses
Ho:p P2 0 versus H2:P1-P2=0
(a) (1 point) Read Section 9.2.1 from the book. and write down the test statistic for the
above hypothesis
(b) Now, suppose random sample of 220 female and 210 male coffee drinkers was
selected and interviewed. The result was that 71 women and 58 men indicated a
preference for decaffeinated coffee.
(i) (2 points) Should we conclude at 5% significance level, that the proportion of
female coffee drinkers who prefer decaffeinated coffee differs from the proportion
of male coffee drinkers who prefer decaffeinated coffee?
(ii) (2 points) Construct 95% confidence interval for the difference in proportions
between male and female coffee drinkers who prefer decaffeinated coffee.
Problem 3. (5 points) To study the effectiveness of certain commercial liquid protein diet,
the Food and Drug Administration sampled nine individuals who were entering two-week
weight loss program. Their weights immediately before and 6 months after completing the
program are recorded below:
Person
Weight before
Weight after
1
197
185
2
212
220
3
188
180
4
226
217
5
170
185
6
194
197
7
233
219
8
166
170
9
205
202
Based on the data, would you conclude that the diet is effective for weight loss? Use 5%
significance level. What assumptions have you made?
Problem 4. (5 points) A study was instigated to see if southern California earthquakes of
at least moderate size (having values of at least 4.4 on the Richter scale) are more likely to
occur on certain days of the week than on others. The following data were obtained for 1100
earthquakes:
Day
Sun
Mon
Tues
Weds
Thurs
Fri
Sat
Number of Earthquakes
156
144
170
158
172
148
152
(a) Test the hypothesis that an earthquake is equally likely to occur on any of the seven
days of the week. Use 5% significance level.
(b) What is the p-value of the data?
Problem 6.
(a) (3 points) A random sample of 187 voters is chosen. and the voters are asked to
evaluate the performance of the first 100 days of the US president. Use the resulting
data to test the hypothesis that the evaluation of an individual does not depend on
whether that individual is man or woman. Use 10% level of significance.
Women Men
Positive evaluation
54
47
Negative evaluation
20
32
Not sure
23
11
(b)
(1 point) Now repeat the exercise in (a). after doubling all the count data.
(c) (1 point) Compare the p-values in (a) and (b). If your answers are different provide
an intuitive explanation for the difference.
Problem 8. An electric utility company wants to estimate the relationship between the
daily summer temperature and the amount of electricity used by its customers The data is
given in the table below:
(a) (2 points) Construct scatter plot for the data.
(b) (2 points) What is the equation of the least squares regression line? Draw the least
squares line on the seatter plot in (a), and compute the R² value for the linear fit.
(c) (2 points) Construct a residual plot and a normal QQ-plot of the residuals, and
comment (qualitatively) on the appropriateness of the linear model assumption
(d) (2 points) Suppose the temperature for tomorrow is predicted to be 93°F Provide
a
point estimate for the amount of electricity that will be consumed tomorrow.
(e) (2 points) Test the hypothesis, at 5% significance level, that the daily temperature
has no effect on the amount of electricity consumed. (Assume the date follow linear
model.)
Temp (F)
Electricity (millions of kW)
85
22.5
90
23.7
76
20.3
91
23.4
84
24.2
94
23.5
88
22.9
85
22.4
97
26.1
86
23.1
82
22.5
78
20.9
77
21.0
83
22.6

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.