For the next few problems, you need only indicate which test you would choose to
ID: 3053204 • Letter: F
Question
For the next few problems, you need only indicate which test you would choose to use and formulate your hypotheses. Do not provide any calculations or conclusions for these problems. (5 pts each)
1. A die is rolled 1100 times and the number rolled is recorded each time. Are the outcomes in line with the expectation of a fair die?
2. A hydrometer is placed in a lab certified mixture and the reading is recorded 100 times. Does the hydrometer seem to be calibrated correctly and ready to be used for other measures?
3. A mathematician claims to have an algorithm for determining how many times red, black, and green will be chosen on the roulette wheel in a random 100 spins. Is there reason to be suspicious of his findings?
4. In a survey of 750 people, responses were recorded about whether each person’s electric bill was above or below $150 and whether they lived on the north, south, east, or west side of the city. Is a person’s geographical area independent of the amount they pay for electricity?
5. A claim was made that a group of students who played at a school soccer game the night before a standardized test would do worse than the rest of the students. To make a determination you compare the mean test score of that group of students with the mean test score of the entire school.
Explanation / Answer
1. Chi square test for multiple proportion
The hypotheses are
H0 : the probability for each face is 1/6
H1 : the observed frequency is not as expected
2. Z test for mean
The hypotheses
H0 : The mean reading is not different from actual reading
H1 : The mean reading is different from actual reading
3. Chi square test for multiple proportion
H0 : the observed frequencies are as expected
H1: the observed frequencies are not as expected
4. Chi square test for independence
H0 : the geographical location is independent of electricity bill they pay
H1 : the geographical location is not independent of electricity bill they pay
5. Z test for mean
H0 : mean score of that group of students is equal to mean score of entire school
H1 : mean score of that group of students is not equal to mean score of entire school