Word Problems
In a study to investigate whether lack of sleep hurts short-term memory, 100 adults were each tested twice. Both times they studied a list of 30 words for two minutes, and were then asked to recall as many as possible, with a different but comparable list used each time. For one of the two tests they had been without sleep for 24 hours, while for the other they had a normal amount of sleep. The order was randomly assigned. The difference in number of words recalled (with sleep – without sleep) was recorded for each person. The average difference was 1.5 words, with a standard deviation of 6.1 words.
1-sample t-test
1-proportion z test
The sample must be reasonably random
The sample must be less than 10% of the population
The sample must be large enough so that: np and nq ≥ 10
You can decrease both 𝛂 and 𝛃 by increasing _____
Sample size
True or false: as 𝛂 increases, 𝛃 decreases.
True
The quality control manager of a large ice-cream manufacturer claims that 80 percent of his 1,000,000 customers are very satisfied with the distribution of chunks in the ice-cream. To test this claim, the local newspaper surveyed 100 customers, using simple random sampling. Among the sampled customers, 73 percent say they are very satisfied. Based on these findings, can we reject the quality control manager’s hypothesis that 80% of the customers are very satisfied?
1-proportion z-test
Difference of means 2-sample t-test
The two samples must be reasonably random and drawn independently
10% condition
Look at a histogram or norm. probability plot of the data. Is it roughly normal?
You can check the nearly normal condition by looking at _______.
Histogram or normal probability plot of the data.
True or false: The power of a test is the probability of correctly failing to reject the null hypothesis
False
Two sections of a class in statistics were taught by two different methods. Students’ scores on a standardized test are shown below. Do the results present evidence of a difference in the effectiveness of the two methods?
2-sample t-test (Matched pairs)
Regression test
Quantitative data and straight enough
Random data
Does the plot thicken?
Nearly normal condition
A _____ error is a false negative.
Type II
True or false: If the 2 samples are independent, you can use a matched pairs test
False
An economist is deriving a model to predict outcomes on the stock market. He creates a list of expected points on the stock market index for the next two weeks. At the close of each day’s trading, he records the actual points on the index. He wants to see how well his model matched what actually happened.
Chi-square goodness of fit test
Chi-square homogeneity
Data are counts
Random/10% condition
Expected cell frequency greater than or equal to 5
For a chi-square test to be fitting for a test of independence, there should be _ variable(s) and _ population(s).
2 variables, 1 population
True or False: If the population standard deviation, σ is known, you can use a z-test on means
True