Which Test
Hypotheses
Miscellaneous
Definitions
Conclusion
100
Jerry wants to see if the amount of alcohol consumed affects how many laughs he gets in one night. He has Kramer collect a random sample at the end of the show about alcohol consumed and laugh rating.
What is Chi-Squared Test of Independence.
100
Zoboomafoo claims that the percentage of antelope who eat at various grasslands are distributed such that 34% like grassland X and grassland Z, 16% like grassland C, 8% like grassland L and grassland BB. In a random sample of 350 antelope, test the claim at the 99% level of confidence. X- 173 Z- 97 C- 32 L- 13 BB- 35
Ho: Px= .34 Pz= .34 Pc= .16 Pl= .08 Pbb=.08 H1: At least one of the proportions is not as claimed. Px= Proportion of antelope who eat at grassland X Pz= Proportion of antelope who eat at grassland Z . . .
100
Jerry made a table specifying favorite night to listen to comedy by gender. Males who preferred Friday Nights: 18 Males who preferred Saturday Early Evening: 11 Males who preferred Saturday Late Nights: 34 Females who preferred Friday Nights: 23 Females who preferred Saturday Early Evening: 13 Females who preferred Saturday Late Nights: 42 What is the expected number of females who prefer Saturday Early Evening.
Row: 11 + 13 = 24 Column: 23 + 13 + 42 = 78 Total = 141 Formula: (24 x 78)/141 = 13.3 females
100
Arnold did a test. It tested the hypothesis that the amount of red, blue, green, and purple tennis balls fit the claimed theoretical distribution at 25% each. Which test did he run?
What is Chi-Squared Goodness of Fit Test?
100
Gus wants to know whether the color of the kickball used during recess is independent of grade level. He marks the grade level of randomly generated kids and the color they use. He runs a chi-squared test of independence and gets a p-value of .098. Explain what the p-value means and help Gus draw a conclusion.
Which means there is a 9.8% chance of getting a more extreme chi-square test statistic relating the color of a kickball to grade level, simply by chance, if the null hypothesis is true. Since 9.8% is greater than 5%, fail to reject Ho Gus should believe that the color of the kickball used during recess is independent of grade level.
200
Ray Rocket wants to see if people in Oahu, Honolulu, and Pearl City buy the same amount of surf boards. His study uses 82 people from Oahu, 79 from Honolulu, and 58 from Pearl City. At the .05 significance, test the claim that the three cities have the same proportion of people buying surf boards.
What is Chi-Squared Test of Homogeneity
200
The school where Arnold goes states that the distribution of colors of kickballs is uniformly distributed. There are 5 different colors of kickballs: red, black, purple, blue, white
Ho: Pr=Pb=Pp=Pbl=Pw= .2 H1: at least one proportion is different than claimed. Pr= proportion of red kickballs Pb=Proportion of black kickballs . . .
200
Will Smith wants to run a study on how many students walk to school versus take the bus to school. He wants to run a test but can't remember if we should run a Homogeneity test or an Independence test. Can you tell him what the differences are?
In a test of independence you are testing whether two characteristics are associated in ONE population. Where in a test of homogeneity you are testing whether the distribution of x is the same for MANY populations. Remember I Owe Him Money.
200
George ran a test which examined whether the phrase "yada yada yada" is independent of gender. Which test did he run?
What is Chi-Squared Test of Independence?
200
Eliza wants to see whether the distribution of gazelle and zebra are the same for both Queensland and Western Australia. With her mom and dad’s help, she obtains a list of how many gazelles and zebras there are in both Australian countries. She runs the test at alpha = .05. The p-value is .059. Explain the p-value and help Eliza determine if there is a difference between Queensland and Western Australia.
Which means there is a 5.9% chance of getting a more extreme chi-squared test statistic comparing the distribution of gazelles and zebras from the two countries; simply by chance, if Ho is true. Since 5.9% is greater than 5% , fail to reject Ho Eliza should believe the distribution of gazelles and zebras is the same for Queensland and Western Australia.
300
Tim Taylor is building a house. He knows that the hammer is the most used tool at 78.4% of the time. He also knows that the saw is used 15.6% of the time and the wrench 6.0%. Out of the 100 times he used a tool he used a hammer 58 times, a saw 29 times, and the wrench 13 times. Does Tim’s usage of tools fit the claimed proportions?
What is Chi-Squared Goodness of Fit Test
300
How are the exercising habits of students related to their parents' exercising habits? Raymond wanted to know for his sports column next week. He surveyed 3450 people from a local sports center.
Ho: Whether a student exercise is independent of whether parents exercise. H1: Whether a student exercises is no independent of whether parents exercise.
300
Sabrina knows that binomial and multinomial situations have 3 things in common and one that is different; however, she can't remember which one is different and which one is the same. Can you help her remember the guidelines for multinomial situations?
* More than 2 outcomes * Fixed number of trials * Events are independent * Probabilities remain the same
300
Sabrina ran a test, which tested whether the distribution of wizards is the same for many populations. What test did she run?
What is Chi-Squared Test of Homogeneity?
300
From previous records the probability of a boy learning how to dance in one day is .08, the probability of learning how to dance in 3 days .15, the probability of learning how to dance in 5 days is .23 and the probability of learning how to dance in 7 days is .54. Doug and 21 other classmates took a 7 day dancing course. Based off of what the dancing instructor noted the following were their results: 3 out of 22 learned in 3 days, 6 learned in 5 days and 10 out of 22 took 7 days to learn how to dance. Would old records still be viable for Doug’s class? Test at alpha = .05.
2 degrees of freedom Cv=5.99 Chi- squared= .4994 Fail to reject Ho At the 95% confidence level, I believe the old records would still work for Doug’s class.
400
Brain knows that 67% of the time vanilla is the favorite type of ice cream. Chocolate is the favorite 23% of the time, and Strawberry is liked 10% of the time. Brain wants to know if his class is different. 5 out of the 30 students liked vanilla, 20 liked chocolate, and 5 liked strawberry.
What is Chi-Squared Goodness of Fit Test.
400
Kramer has invented the "Bro" and is looking for an agency to buy his idea. He wants to see if 3 different places take in the same amount of new ideas.
Ho: The distribution of accepting new products is the same for the 3 agencies. H1: The distribution of accepting new products is NOT the same for the 3 agencies.
400
Raymond ran a test, but not all of his expected numbers were bigger than five to continue on. He doesn't know what to do next, so can you help him?
He would need to condense the columns that are not bigger than five, and re-do his observed and expected tables again.
400
Will needs to find the degrees of freedom for a chi-squared test of homogeneity, but he can't remember how to do it. Can you tell him how?
Row minus one times column minus one equals degrees of freedom. (r-1)(c-1)
400
Didi Pickles wants to know whether the number of Reptar bars eaten affects how long of a nap kids take. She has Stu run a chi-square test of independence which yields a p-value of .04. Help Stu and Didi draw a conclusion.
Since 4% is less than 5%, reject Ho They should believe that the number of Reptar bars eaten is not independent of how long of a nap a kid takes.
500
Zoboomafoo wants to see if there is a difference in preference in watering holes between the tigers, the lions, and the bears. (Oh my) Out of the two watering holes (Victoria and Turkana) 30 of the Tigers preferred Victoria and 7 preferred Turkana. 20 Lions preferred Victoria, and 28 preferred Turkana. 13 Bears preferred Victoria and 35 preferred Turkana. Test the claim that the three different types of animals have the same preference of watering hole.
What is Chi-Squared Test of Homogeneity.
500
Raymond wants to see if some college football teams work harder than the others. He doesn't want anyone saying that one team is better than the other just because more of their players go to the pros. Raymond surveyed 4 Big Ten teams which were randomly chosen. Test the claim that all 4 Big Ten teams produce the same proportion of athletes who go to the pros.
Ho: The distribution of athletes who go to the pros is the same for all 4 Big Ten teams. H1: The distribution of athletes who go to the pros is NOT the same for all 4 Big Ten teams.
500
Sabrina is trying to study for her AP Stats test and hates problems like these, can you tell her which one of these is the right answer so she can pass her test? Which one of these is false. A. The smaller the resulting chi-squard value, the better the fit. B. The P-value is the probability of obtaining a chi-squared value as extreme as the one obtained if the null hypothesis is assumed true. C. A chi-squared distribution is not symmetric, and is always skewed right. D. The larger the degrees of freedom value, the closer the chi-squared distribution to a normal distribution. E. None are false, all are true
E. None are false, all are true.
500
Raymond ran a test and wants to put it in the newspaper. What can he not do even if there is sufficient evidence to reject the null hypothesis of independence?
He cannot necessarily claim any direct causal relationship. He can make a statement about some link or relationship between variables, he is NOT justified in claiming that one causes the other.
500
Arnold and Gerald want to know whether rating of their cheese for the Cheese Festival is the same for both boys and girls at P.S. 118. They randomly survey 50 girls and 50 boys. This is what their results look like with 1 being the worst rating and 4 being the best rating. Males who gave them a 1: 6; a 2: 14; a 3: 13; and a 4: 17. Females who gave them a 1: 15; a 2: 5; a 3: 22; and a 4: 8 They can’t remember what to do next with the data they have collected. They need your help to see if there is a difference between the two populations. (They want to test at the 95% confidence level.)
Degrees of freedom: 3 CV=7.81 Chi-square test statistic= 13.67 Reject Ho At the 95% confidence level, I believe the distribution of ratings of Arnold and Gerald’s cheese is not the same for both boys and girls.
M
e
n
u