Homework Problem Example for Week 6

1. Examples for Week 6
Homework Problems 17,18 and 20
B Heard

2. Example for Week 6
Homework Problem 17
B Heard

3. Week 6 Homework Examples
• This one is just a confidence interval problem.
• Example
– In a survey of 6000 men, 3695 say they wore a hat
at least once a week. Construct a 95% confidence
interval for the population proportion of men who
wore a hat at least once a week.

4. Week 6 Homework Examples
• Minitab >> Stat >> Basic Statistics >> 1 Proportion,
input number of events & number of trials
Check this box

5. Week 6 Homework Examples
• Answer in session window, rounded to three
decimal places, it would be (0.603,0.628)

6. Example for Week 6
Homework Problem 18
B Heard

7. Week 6 Homework Examples
• This one is a sample size problem.
• Example
– A researcher wishes to estimate with 99% confidence,
the proportion of adults who have high speed Internet
access. The researcher’s estimate must be accurate
within 5% of the true proportion.
– a) Find the minimum sample size needed using a prior
study that found 65% of the respondents said they
have high speed Internet access.
– b) Find the minimum sample size needed assuming
that no preliminary estimate is available.

8. Week 6 Homework Examples
• Just use the equation
Commonly Used Zc Values
Confidence
z
90%
1.645
95%
1.96
99%
2.575

9. Week 6 Homework Examples
• a) Find the minimum sample size needed using a
prior study that found 65% of the respondents said
they have high speed Internet access.
n = (0.65)(1-0.65)(2.575/0.05)^2
n = (0.65)(0.35)(2.575/0.05)^2
n = 603.3869
So the sample size would be
Confidence
604 (ALWAYS ROUND SAMPLE
90%
SIZES UP)
95%
99%
z
1.645
1.96
2.575

10. Week 6 Homework Examples
• b) Find the minimum sample size needed
assuming that no preliminary estimate is
available. (USE 0.5 WHEN NO ESTIMATE IS
AVAILABLE)
n = (0.5)(1-0.5)(2.575/0.05)^2
n = (0.5)(0.5)(2.575/0.05)^2
n = 663.0625
Confidence
So the sample size would be
664 (ALWAYS ROUND SAMPLE
90%
SIZES UP)
95%
99%
z
1.645
1.96
2.575

11. Example for Week 6
Homework Problem 20
B Heard

12. Week 6 Homework Examples
• This one is a confidence interval for a proportion.
• Example
– The table shows the results of a survey in which
separate samples of 500 adults each from the East,
South, Midwest and West were asked if traffic
congestion is a serious problem in their community.
Complete parts a and b.
• a) Construct a 95% confidence interval for the proportion of
adults from the Midwest who say traffic congestion is a
problem.
• b) Construct a 95% confidence interval for the proportion of
adults from the West who say traffic congestion is a
problem.

13. Week 6 Homework Examples
In my example there were 500
samples from each geographic
area. So that would mean 175
out of 500 in the East, 165 out
of 500 in the South, 125 out of
500 in the Midwest and 265
out of 500 in the West.
(Remember they were
separate samples)
I get these numbers just by
multiplying, for example for
the East, 0.35*500 = 175

14. Week 6 Homework Examples
– a) Construct a 95% confidence interval for the
proportion of adults from the Midwest who say
traffic congestion is a problem.
– Go to Minitab >> Stat >> Basic Statistics >> 1
Proportion

15. Week 6 Homework Examples
125 out of 500 is
25% for the
Midwest
Very
Important
that you
check this
box

16. Week 6 Homework Examples
• Answer
Rounded to three decimal
places, the answer would
be (0.212, 0.288)

17. Week 6 Homework Examples
– b) Construct a 95% confidence interval for the
proportion of adults from the West who say traffic
congestion is a problem.
– Go to Minitab >> Stat >> Basic Statistics >> 1
Proportion

18. Week 6 Homework Examples
265 out of 500 is
53% for the
West
Very
Important
that you
check this
box

19. Week 6 Homework Examples
• Answer
Rounded to three decimal
places, the answer would
be (0.486,0.574)