Practice problems for homework 5

Contingency problem practice.

Bayesian contingency practice.

Frequency and relative frequency.

Using RANDI(1,10) on the TI-30XIIs a number of times, I get these frequencies. Find n and the relative frequencies, written as exact decimals.

f(1) = 7
f(2) = 7
f(3) = 6
f(4) = 6
f(5) = 3
f(6) = 2
f(7) = 5
f(8) = 5
f(9) = 6
f(10) = 3

Answers to last part in comments.

Answers to quiz 4

Round all numbers that aren’t whole numbers except proportions to two places after the decimal.
Round proportions to four places after the decimal, like the number in the z-score tables.

(14 points)
Sample of 20 pulse rates for women:
97, 88, 83, 77, 60, 78, 73, 67, 72, 82, 70, 67, 60, 80, 90, 100, 69, 80, 60, 68

n = 20 x-bar = 76.05 sx = 11.66


median = __75___ z(median) = ___-.05___ Test okay? __yes___


Proportion for z(high) = _.9798_ Proportion for z(low) = _.0838_
Test okay? __yes___


If both tests are okay, continue to the 95% confidence interval for µx.
CLM95% = _2.093___


From this sample, we are 95% confident the true average µx of women’s pulse rates is between 70.59 and 81.51.

Finding the confidence interval for sigmax using df = n – 1 and sx is sx*sqrt((n-1)/chi-squareleft) > sigmax > sx*sqrt((n-1)/chi-squareright)
(6 points)
For this sample find the endpoints for 95% confidence.

chi-squareleft= _8.907__ chi-squareright = __32.852__


We are 95% confident given this sample that the true standard deviation of the population of women’s pulse rates is between _8.87__ and __17.03__.

Practice problems for homework 4

Here is a sample of pulse rates for females.

100, 97, 90, 88, 83, 82, 80, 80, 78, 77, 73, 72, 70, 69, 68, 67, 67, 60, 60, 60

1) Find n, x-bar, sx and the median.

2) Is -0.5 < z(median) < 0.5?

3) is proportion(z(high)) - proportion(z(low)) > 88%?

4) If yes to both question 2) and question 3), Find the 95% confidence interval for mux, where the endpoints are rounded to one place after the decimal point.

5) Find the 95% confidence interval for sigmax.

Answers in the comments.

Answers to quiz 3

Round z-scores to two places after the decimal. Round proportions to four places after the decimal.

(6 points) The heights of men as a population is normally distributed, with mux= 69.0” and sigmax= 2.8”.

What is the z-score for 5’6”? ANSWER: -1.07
What proportion does this correspond to? ANSWER: .1423 (TI-83 ANSWER: .1420)

What is the z-score for 6’0”?
What proportion does this correspond to? ANSWER: .8577 (TI-83 ANSWER: .8580)

What percentage of men are between 5’6” and 6’0”? ANSWER: .7154 (TI-83 ANSWER: .7160)

(6 points) Assume we have a data set where mux= 10 and sigmax= 2.5. Use the Central Limit Theorem formula to find the answers to the following questions.

What is the z-score of a sample where x-bar = 8.3 and n = 12 and what proportion does it correspond to?

z-score = ANSWER: -2.36
proportion = ANSWER: .0091

Thanks to Daniel Barreto for pointing out my error in the first answer I posted.

What is the z-score of a sample where x-bar = 10.2 and n = 40 and what proportion does it correspond to?

z-score = ANSWER: 0.51
proportion = ANSWER: .6950 (TI-83 ANSWER: .6936)

What proportion does x = 13 correspond to? (Single sample)
Answer: .8849

(8 points) Consider the number of theaters list on the blue handout. Find the number of units in each category, f(x) and find the relative frequency p(x) = f(x)/n for each of these numerical intervals. Write relative frequency as percentages. Draw a horizontal bar chart using the template provided.

Interval ___ frequency relative frequency

Under 3500 10_________40%

3500-4000 7__________28%

Over 4000 8 __________32%

__________0%-------10%------20%------30%---------40%

Under 3500XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

3500-4000_XXXXXXXXXXXXXXXXXXXXXXXXXXX

Over 4000_XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Practice problems for homework 3

For pregnancies, assume mux = 280.6 days and sigmax = 9.7 days.

a. What is the z-score for 273 days?
b. What is the proportion that corresponds to 273 days?
c. What is the z-score for 288 days?
d. What is the proportion that corresponds to 288 days?
e. What proportion of pregnancies last between 273 to 288 days?





With the Central Limit Theorem, we need to know the average and standard deviation of a population and the average and size of a sample, x-bar and n, respectively. This gives us a z-score which corresponds to a proportion.

f. What is the z-score for 273 days for a sample where n = 8?
g. What is the proportion that corresponds to 273 days for a sample where n = 8?
h. What is the z-score for 288 days for a sample where n = 8?
i. What is the proportion that corresponds to 288 days for a sample where n = 8?
j. What proportion of pregnancies last between 273 to 288 days for a sample where n = 8?

Consider the following data set.

17, 19, 19, 18, 19, 19, 15, 20, 20, 20, 20, 14, 18, 20, 19, 20, 18, 19, 20, 16

Find the frequencies and relative frequencies for each value.

Answers in the comments.

Answers to quiz from 9/11

(10 points) On any single section of the SAT, mux = 500 and sx = 100. Find the z-scores for the following raw SAT scores and use the look-up table to find what proportion of the people taking the SAT will get a score that is less than or equal to the given score. Z-scores should be rounded to two places after the decimal and the proportions from the table are written to four decimal places.

SAT score: 570
z-score = .7
proportion at that z-score or less = .7580

SAT score: 750
z-score = 2.5
proportion at that z-score or less = .9938

SAT score: 395
z-score = -1.05
proportion at that z-score or less = .1469

SAT score: 625
z-score = 1.25
proportion at that z-score or less = .8944

SAT score: 490
z-score = -0.1
proportion at that z-score or less = .4602


(6 points) For the following movie studios find the average number of theaters on the opening weekend for the movies they made that were in the top 25 grossing movies of 2009 and find the median number of theaters of those sets of films. Round the answers to the nearest tenth.


Fox
Average number of theaters 3771.5
Median number of theaters 3898
Numbers on list: 3452, 3700, 4099, 4099, 4096, 3183


Sony
Average number of theaters 3298.5
Median number of theaters 3274
Numbers on list: 3404, 3144, 3527, 3119

WB
Average number of theaters 3572
Median number of theaters 3530
Numbers on list: 4325, 3269, 3110, 3626, 3530
(1 point each)
What movie had the biggest opening weekend?
The Twilight Saga: New Moon

What month had the most opening days on the list?
May (6)

What movie on the list opened earliest in the year?
Paul Blart: Mall Cop, Jan. 16

What movie on the list opened latest in the year?
Sherlock Holmes, Dec. 25

Practice problems for homework 2

Find the following statistics following set of data. Round all answers to two place after the decimal, except the proportions, which are given on the table to four places after the decimal

z(x) = (x - x-bar)/sx

17.41, 18.22, 19.17, 17.87, 18.15, 17.86, 18.12, 17.97, 18.46, 18.14

x-bar = ______

sx = _______

z(high) = _____ Proportion associated = ______

z(low) = _____ Proportion associated = _______

For the following movie studios, find the average opening weekend for the movies that were in the total opening weekend receipts for the same films. Round the answers to the nearest million dollars.

Average opening weekend for Fox: _________

Total opening weekend for Fox: ___________


Average opening weekend for WB: _________

Total opening weekend for WB: ___________


Average opening weekend for BV: _________

Total opening weekend for BV: ___________


Answers in the comments.

Answers to quiz from 9/6

Consider the total gross variable of the top 25 movies from 2009 (numbers on the blue sheet).
(12 points) Find the following statistics. Round all answers to the nearest million dollars. Don’t forget the dollar signs.

high = $749,000,000
Q3 = $268,000,000
Q2 (or median) = $180,000,000
Q1 = $146,000,000
low = $121,000,000
IQR = Q3 – Q1 = $122,000,000
High outlier threshold = $451,000,000
Low outlier threshold =-$37,000,000

Is there any outlying data and if so, what is it? Answer: Yes, Avatar at $749,000,000 is an outlier.


(8 points) The data set below is written in stem and leaf form.

14|3
13|
12|
11|
10|8
_9|
_8|5
_7|1578
_6|248
_5|559
_4|23569
_3|002448
_2|5

Find the following statistics. Round any decimal number to the nearest tenth.

n = 25
High = 143
Q3 = 73
Q2 = 55
Q1 =36
Low = 25
x-bar = 57.9
mode = 30, 34, 55

Reminders for this week.

1. Homework is due by noon on Friday. You can turn it in to my mailbox in the math lab G-201 or you can send it by e-mail to mhubbard@peralta.edu. If you turn it in electronically, you should print out a copy for your own records. I'll be handing out a copy of the correct answers to the people who turn it in online with marks indicating where the differences are.

2. YOU MUST HAVE A CALCULATOR BY THE NEXT CLASS PERIOD. Mark and I will be showing people how to input data sets using the TI-83/84 style calculators as well as the TI-30XIIs and other calculators people may have.

3. See you on Saturday. Send any questions you have to mhubbard@peralta.edu.