1. A teacher is experimenting with computer-based instruction. In which situation could the teacher use a hypothesis test for a population mean?
A. She gives each student a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a posttest. The teacher wants to see if the difference in scores will show an improvement.
B. The teacher uses a combination of traditional methods and computer-based instruction. She asks students if they liked computer-based instruction. She wants to determine if the majority prefer the computer-based instruction.
C. She randomly divides the class into two groups. One group receives computer-based instruction. The other group receives traditional instruction without computers. After instruction, each student has to solve a single problem. The teachers wants to compare the proportion of each group who can solve the problem.
2. A medical researcher wants to measure the effects of a new drug on cholesterol levels using a hypothesis test. The target is a 30-point decrease in cholesterol levels after a treatment cycle. The researcher takes a random sample of patients and measures their cholesterol levels before and after a treatment cycle of the drug.
Which type of hypothesis test should they use?
A. test for a difference in two population proportions
B. test for one population proportion
C. test for one population mean
D. test for a difference in two population means
3. A marketing student is estimating the average amount of money that students at a large university spent on sporting events last year. He asks a random sample of 50 students at one of the university football games how much they spent on sporting events last year. Using this data he computes a 90% confidence interval, which turns out to be ($217, $677).
Which one of the following conclusions is valid?
A. 90% of the sample said they spent between $217 and $677 at sporting events last year.We can be 90% confident that the mean amount of money spent at sporting
B. events last year by all the students at this university is between $217 and $677.
C. No conclusion can be drawn.
4. The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour. When wheat is ground into flour, insects that were in the wheat are ground up as well.
The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption.
The null hypothesis is that the mean number of insect parts per 100 grams is 75. The alternative hypothesis is that the mean number of insect parts per 100 grams is greater than 75.
Is the following a Type I error or a Type II error or neither?
The test fails to show that the mean number of insect parts is greater than 75 per 100 grams when it is.
Type II error
Type I error
5. In a fictional study, suppose that a psychologist is studying the effect of daily meditation on resting heart rate. The psychologist believes the patients who not meditate have a higher resting heart rate. For a random sample of 45 pairs of identical twins, the psychologist randomly assigns one twin to one of two treatments. One twin in each pair meditates daily for one week, while the other twin does not meditate. At the end of the week, the psychologist measures the resting heart rate of each twin. Assume the mean resting heart rate is 80 heart beats per minute.
The psychologist conducts a T-test for the mean of the differences in heart rate of patients who do not meditate minus resting heart rate of patients who do meditate.
Which of the following is the correct null and alternative hypothesis for the psychologist's study?
H0: µ = 80; Ha: µ > 80
H0: µ = 0; Ha: µ > 0
H0: µ = 0; Ha: µ ≠ 0