Problem Set 2 - Part 2

Stat 102 Problem Set 2: Part 2
Instructions:
1. The problem set should be answered individually. Exercise academic honesty

always. Do not share copy of the questions or your answers to classmates who have
not yet answered the problem set.
2. All answers should be hand-written on a bond paper. Write your name and indicate
your section. Write your answers neatly and legibly.
3. Scan your paper and submit it as a pdf file, or if you don’t have a scanner, take a
clear picture of your paper. If you have multiple pages/pictures combine them into one
pdf file. Make sure that your pictures are clear, and your answers and solutions can
be clearly read. Use the format <last name>_PS2_Stat102<section> for your file name
(example: Montes_PS2_Stat102C.pdf).
4. There is no time limit for part 2, but it should be submitted before the indicated due
date and time. Late submissions will not be accepted.
Answer the following questions. Show all solutions if applicable. For hypothesis
tests, include a) Null and alternative hypotheses, b) Critical Value, c) Test
Statistic Value d) Decision and Conclusion. Maximum points: 30 points
1. The head of the Philippine University (PU) observes a decline on the alcoholic
expenditures of the students from a monthly expenditure of 350 pesos in the
previous year. To check on this, he randomly selected 10 PU students who drink
alcoholic beverages and asked of the amount, in pesos, that they usually spent on
alcoholic beverages in a month. It is known that the usual amount spent on
alcoholic beverages by the students who drink alcoholic beverages follows the
normal distribution with standard deviation of 10 pesos. The data collected are:
400, 235, 200, 250, 200, 300, 500, 430, 420, and 220. Construct and interpret a
95% confidence interval for the true mean amount spent by the students on
alcoholic beverages. (4 points)
2. The CEO of a large supermarket chain in the National Capital Region is claiming
to be paying its contractual higher than the minimum daily wage rate of 500 pesos.
To check on this claim, a labour union leader obtained a random sample of 144
contractual employees from this supermarket chain and their daily wage earnings
resulted to an average wage of 510 pesos per day with standard deviation of 100
pesos. The daily wage of the region is assumed to follow a distribution with an
unknown population variance. Perform a test of hypothesis at 5% level of
significance to help the labour union leader in making an empirical-based
conclusion regarding the CEO’s claim. 6 points.
3. An independent research group is interested to show that the percentage of babies

delivered through Cesarean Section is decreasing. For the past years, 20% of the
babies were delivered through Cesarean Section. The research group randomly
inspects the medical records of 144 births and finds that 25 of the births were by
Cesarean Section. Can the research group conclude that the percent of births by
Cesarean Section has decreased at 0.05 level of significance? 6 points
4. A farmer wants to test three brands of weight-gain diets for chickens to determine
if the mean weight gain for each of these brands is the same. He selected 15
chickens and randomly put each of them on one of these three brands of diet. The
following table lists the weights (in pounds) gained by these chickens after a period
of 1 month.
At the 1% significance level, can you conclude that the mean weight gain for all
chickens is the same for each of these three diets? 7 points
Note: Under c) Test Statistic Value include the F anova table.
5. In a study of the performance of a computer printer, the size (in kilobytes) and the
printing time (in seconds) for each of 22 small text files were recorded. A regression
line was a satisfactory description of the relationship between size and printing
time. The results of the regression analysis are shown below.
Coefficients Standard Error t-stat P-value

Intercept 11.6559 0.3153 37 <0.0001
Size 3.47812 0.294 11.8 <0.0001
Regression Statistics
R Square 0.875
Adjusted R Square 0.869
Standard error 0.6174
Observations 22
a. Write down the regression equation. 2 points
b. Interpret the slope of the regression equation (b1). 2 points
c. Interpret the value of for R-squared. 2 points
d. Is size a significant factor in predicting the printing time? Support your answer
using the output. 2 points
e. Use the regression equation to predict the printing time of a printer if size is
80kb. 2 points

Problem Set 2 - Part 2

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Stat 102 Problem Set 2: Part 2

1. The problem set should be answered individually. Exercise academic honesty

3. An independent research group is interested to show that the percentage of babies

Coefficients Standard Error t-stat P-value

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