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?
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.
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.
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.
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
$a=0\text{.}\text{05}$ ; Conclusion: Local data do not fit the AP Examinee Distribution. Decision: Do not reject null when
$a=0\text{.}\text{01}$ ; Conclusion: There is insufficient evidence to conclude that Local data do not fit the AP Examinee Distribution.
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.
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?
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
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.
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)=
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.