Name that test!
We want to test whether or not the proportion of residents in a certain county who support a certain law is equal to 60%. A survey of a random sample of 100 residents was conducted and showed that the sample proportion was .64. What test should be performed?
1-proportion z-test
TEST: 1-prop z-test
random: randomly selected
independence: n=30, population= 200
sample size: p=.45
not met, 10x sample size is less than population
Contingency table of the handedness of a sample of Americans and Canadians
Right-handed Left-handed
American 236 19
Canadian 157 16
What test would be used to test whether these observed frequencies are significantly different from the frequencies expected is handedness is unrelated to nationality?
alpha level: 5%
p-value: .045
Can we reject the null hypothesis?
Yes, p-value is less than alpha level, so the results are significantly different.
A local pet shop is trying to determine what percent of the U.S. population prefers dogs to cats. Last week they surveyed the 274 people who entered the store. Of those 274 people, 183 people prefer dogs to cats. Create a 95% confidence interval to estimate the true percentage of U.S. residences who prefer dogs to cats. What would the formula for this test be?
.67 +- 1.96 sqroot((.67*.33)/274)
A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results from randomly selected subjects are shown in a table with data representing pain levels before and after. A lower score indicates less pain. Are the sensory measurements, on average, lower after hypnotism? What test would be used to evaluate this data?
matched pairs t-test
TEST: 2-sample T-test
random: randomly selected
independent:n= 68, population= 10,000
normal: n=68
samples are independent of each other
conditions met
Is gender independent of education level? A random sample of 395 people was surveyed and each person was asked to report the highest education level they obtained. The data that resulted from the survey are summarized in the following table:
High School Bachelors Masters. Ph.d. Total
Female 60 54 46 41 201
Male 40 44 53 57 194
Total 100 98 99 98 395
What could be used to see if there is a relationship between gender and the level of education they have obtained?
x2 test for independence
alpha level: 10%
p-value: .103
Should we reject the null hypothesis?
No, p-value is higher than alpha level.
Kylie suspected that when people exercise longer, their body temperatures change. She randomly assigned people to exercise for 30 or 60 minutes, then measured their temperatures. The 18 people who exercised for 30 minutes had a mean temperature of 38.3 degrees C with a standard deviation of .27 degrees C. The 24 people who exercised 60 minutes had a mean temperature of 38.9 degrees C with standard deviation .29 degrees C.
Kylie wants to estimate the difference in the mean body temperature after exercising for the two amounts of time (30 min- 60 min). Assume all conditions have been met. What would give us the confidence interval of mean of 30- mean of 60?
-.6 +- t*sqroot ((.272/18)+(.292/24))
We want to test whether the mean weight between two different species of turtles is equal. A random sample of turtles from each population was weighed. The results from sample 1 of 40 turtles showed an average weight of 300g with a standard deviation of 18.5g. The results from sample 2 of 38 turtles showed an average weight of 305g with a standard deviation of 16.7g. What test would be best to determine if the mean weight is equal?
2-sample T-test
TEST:x2 goodness of fit
random: census
population: n=46, population= 5,000
expected values: 5, 8, 12, 4, 15, 23, 7
not met, not all expected values greater than 5
Flavor Number of Pieces of Candy (10 bags) Expected Number of Pieces of Candy
Apple 180 200
Lime 250 200
Cherry 120 200
Lemon 225 200
Grape 225 200
What test could be used to analyze if there is a significant different between the observed and expected values?
x2 goodness of fit
A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim, a random sample of 100 doctors is obtained. Of these 100 doctors, 82 indicate that they recommend aspirin. Is this claim accurate? Use alpha = 0.05.
Plug this data into your calculator, would you be able to reject the null?
You’re testing two flu drugs A and B. Drug A works on 41 people out of a sample of 195. Drug B works on 351 people in a sample of 605. Are the two drugs comparable? Use a 5% alpha level. What would be the appropriate formula for this test?
Z= (.21-.58)/sqroot(.49(.51)(1/195 + 1/605)
A random sample of 400 college freshmen, 200 men and 200 women, were each asked which of the following movies they liked best: The Terminator, The Princess Bride, or The Lego Movie. The results are displayed in a contingency table. Is the distribution among men and women the same for which movies they like best? What test could be used to determine this?
TEST: 1-sample T-test
random: given
independence: n=25, population= 3,000
normal: normal quantile plot shows fan shape
not met, normal quantile plot does not show linear correlation
Category Observed Test Proportion Expected Contribution to Chi-Sq
Hearts 13 0.25 10 0.9
Diamonds 8 0.25 10 0.4
Spades 8 0.25 10 0.4
Clubs. 11 0.25 10 0.1
Which test is best?
x2 goodness of fit
A random sample of 36 teens finds they sent an average of 53 texts yesterday with a std dev of 15. A different random sample of 32 20-somethings found an average of 75 texts with std dev of 19. Testing at the 4% level, does it look like 20-somethings send more texts than teens?
Plug this into your calculator, should you reject the null?
Yes, p-value of 0 is less than .04.
X2 = Σ(O-E)2 / E
A car manufacturer aims to improve the quality of the products by reducing the defects and also increase the customer satisfaction. Therefore, he monitors the efficiency of two assembly lines in the shop floor. In line A there are 18 defects reported out of 200 samples. While the line B shows 25 defects out of 600 cars. At a 5% confidence level, is the differences between two assembly procedures are significant? What test can be used to determine this?
2-proportion z-test
How many pleats does a chef's hat have?
100
A university admissions officer was concerned that males and females were accepted at different rates into the four different schools (business, engineering, liberal arts, and science) at her university. She collected the following data on the acceptance of 1200 males and 800 females who applied to the university:
#(Acceptances) Business. Engineer Lib Arts. Science (FIXED) Total
Male 300 (25%) 240 (20%) 300 (25%) 360 (30%) 1200
Female 200 (25%) 160 (20%) 200 (25%) 240 (30%) 800
Total 500 (25%) 400 (20%) 500 (25%). 600 (30%) 2000
Are males and females distributed equally among the various schools? Which x2 test would be able to answer this question?
x2 test for homogeneity
Chicks of a certain type of bird are supposed to exhibit four different phenotypes in a 1:4:4:9 ratio. A recent SRS of 200 chicks found the following:
phenotype: A B C D
count: 15 56 45 84
expected: 11.11 44.44 44.44 100
Plug this data into your calculator, should the null be rejected testing at the 5% level?
No, p-value of .074 is greater than .05.
Researchers wanted to see if people who exercise regularly sleep better than people who don't. They took a random sample of adult males and surveyed them about their exercise routine and their sleep duration. Here is a summary of the results:
exercise no exercise
mean: 7h 6.5 h
SD: 1h 1.5h
# of people: 180 190
The researchers want to use these results to test: H0: difference=0. HA: mean exercise-mean no exercise is greater than 0. Assume all conditions have been met. What would be the formula for this test?
t= (7-6.5)/sqroot ((12/180)+(1.52/190))