<< Chapter < Page Chapter >> Page >
This module provides homework on Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
  • Explain why the “goodness of fit” test and the “test for independence” are generally right tailed tests.
  • If you did a left-tailed test, what would you be testing?
Got questions? Get instant answers now!

Word problems

For each word problem, use a solution sheet to solve the hypothesis test problem. Go to The Table of Contents 14. Appendix for the chi-square solution sheet. Round expected frequency to two decimal places.

A 6-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test to determine if the die is fair. The data below are the result of the 120 rolls.

Face Value Frequency Expected Frequency
1 15
2 29
3 16
4 15
5 30
6 15
Got questions? Get instant answers now!

The marital status distribution of the U.S. male population, age 15 and older, is as shown below. ( Source: U.S. Census Bureau, Current Population Reports )

Marital Status Percent Expected Frequency
never married 31.3
married 56.1
widowed 2.5
divorced/separated 10.1

Suppose that a random sample of 400 U.S. young adult males, 18 – 24 years old, yielded the following frequency distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult population. Calculate the frequency one would expect when surveying 400 people. Fill in the above table, rounding to two decimal places.

Marital Status Frequency
never married 140
married 238
widowed 2
divorced/separated 20
  • The data fits the distribution
  • The data does not fit the distribution
  • 3
  • 19.27
  • 0.0002
  • Decision: Reject Null; Conclusion: Data does not fit the distribution.
Got questions? Get instant answers now!

The next two questions refer to the following information . The columns in the chart below contain the Race/Ethnicity of U.S. Public Schools for a recent year, the percentages for the Advanced Placement Examinee Population for that class and the Overall Student Population. ( Source: http://www.collegeboard.com ). Suppose the right column contains the result of a survey of 1000 local students from that year who took an AP Exam.

Race/Ethnicity AP Examinee Population Overall Student Population Survey Frequency
Asian, Asian American or Pacific Islander 10.2% 5.4% 113
Black or African American 8.2% 14.5% 94
Hispanic or Latino 15.5% 15.9% 136
American Indian or Alaska Native 0.6% 1.2% 10
White 59.4% 61.6% 604
Not reported/other 6.1% 1.4% 43

Perform a goodness-of-fit test to determine whether the local results follow the distribution of the U. S. Overall Student Population based on ethnicity.

Got questions? Get instant answers now!

Perform a goodness-of-fit test to determine whether the local results follow the distribution of U. S. AP Examinee Population, based on ethnicity.

  • 5
  • 13.4
  • 0.0199
  • Decision: Reject null when a = 0 . 05 size 12{a=0 "." "05"} {} ; Conclusion: Local data do not fit the AP Examinee Distribution. Decision: Do not reject null when a = 0 . 01 size 12{a=0 "." "01"} {} ; Conclusion: There is insufficient evidence to conclude that Local data do not fit the AP Examinee Distribution.
Got questions? Get instant answers now!

The City of South Lake Tahoe, CA, has an Asian population of 1419 people, out of a total population of 23,609 ( Source: U.S. Census Bureau ). Suppose that a survey of 1419 self-reported Asians in Manhattan, NY, area yielded the data in the table below. Conduct a goodness of fit test to determine if the self-reported sub-groups of Asians in the Manhattan area fit that of the Lake Tahoe area.

Race Lake Tahoe Frequency Manhattan Frequency
Asian Indian 131 174
Chinese 118 557
Filipino 1045 518
Japanese 80 54
Korean 12 29
Vietnamese 9 21
Other 24 66
Got questions? Get instant answers now!

Questions & Answers

An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Adu
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.
Nerisha Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics' conversation and receive update notifications?

Ask