MBA 602 Individual Homework
Problem 1 A field goal kicker of an NFL team makes 30 % of field goals
over 50 yards.
a) (page 13) He makes 20 trials in a season and each trial is independent.
What is the average number of field goals over 50 yards he makes in a season?
What is the standard deviation of the number of field goals over 50 yards he
makes in a season?
b) (page 23) When X denotes the number of field goals over 50 yards in n
independent trials, the sample proportion is p = X . When n = 1000, which
ˆ n
X
means that it is very large, what is the approximate distribution of p = 1000 ?
ˆ
Problem 2 (Example 2)The weigh of a pineapple sold in Great Cardinals
Supermarket follows Normal distribution with mean 5 pounds and standard
deviation 1.5. When Ross bought a pineapple from it, what is the probability
that the weight of it is between 4 and 7 pounds?
Problem 3 (Problem 2 continued, Example 3,4) Chandler bought 16 pineapples from the supermarket and calculated the average weight of them. What
is the probability that the average weight is between 4.5 and 5.2 pounds?
1
Problem 4 (Example 5) Joey bought 16 pineapples from Sleepy Wildcat
Supermarket and the average weight of them was 4.5 It is known that the
population standard deviation is 1.5. Find the 95 % confidence interval for
the true (population) average weight.
Problem 5 (Example 6) A survey of 225 people shows that 185 people like
a new Jupiter X smartphone. Find the 95 % confidence interval for the true
proportion of people who like it.
Problem 6 (Example 7,8) Professor Kiss-up promised that the length of his
lecture would follow Normal distribution with mean 50 minutes and standard
deviation 6 minutes. Rachel was so bored in his classes, measured the length
of lectures 64 times, and got a sample mean 52 minutes. Find the test
statistic and the p-value of the test H0 : Average length of his lecture is 50
minutes vs. H1 : Average length of his lecture is more than 50 minutes. (Use
Z test instead of t test.)
Problem 7 (Example 9)Professor Kiss-up also promised that 50 % of the
students would get an A in his class. In his NBA 206 class, 45 out of 100
students got an A. Find the test statistic and the p-value of the test H0 : The
proportion of A is 50 %. vs. H1 : The proportion of A is not 50 %.
2
Problem 8 (page 55) The following is an ANOVA table of a multiple regression. The number of observations is 100.
Table 1: ANOVA table
Source SS df MS F p-value
Model
a
b
d
f
0.00
Error
30 96
e
Total 300 c
a) Find a,b,c,d,e,f.
b) What percent of variation is explained by the regression line?
c) What is the estimator of σ 2 , the variance of the error term?
d) Write the null hypothesis of the F-test.
3
