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Exam 3 – Math 140
Each question is worth 3 points
Form B
1. When does a confidence interval and a hypothesis test produce the same results?
a. When you have a one-tailed alternative hypothesis.
b. When you have a two-tailed alternative hypothesis.
c. When you have a large sample size.
d. When you have a small sample size.
e. They never produce the same results.
2. What does the notation, 𝜇, indicate?
a. Sample mean.
b. Population mean.
c. Sample standard deviation.
d. Population standard deviation.
e. Sample proportion.
3. What is the most common level of significance used?
a. 0.10
b. 0.05
c. 0.01
d. 0.50
e. 0
4. When a confidence interval for the difference of two population means doesn’t contain 0, what can be concluded?
a.
b.
c.
d.
e.
The results are inconclusive.
An error was made in the calculation.
The population means may be significantly different.
The population means may be the same.
The population means must the same.
5. Which of the following is not an indicator of dependent samples?
a.
b.
c.
d.
e.
Objects in the sample are measured twice.
Objects in the sample are related somehow (like twins).
Both samples are randomly taken from their populations, and the samples are not paired.
Experimenters have deliberately matched subjects in groups to have similar characteristics.
All of the above are indicators of dependent samples.
6. What is the practice of stating a hypothesis after first looking at the data?
a. Data bias.
b. Data mining.
c. Data analysis.
d. Data dredging.
e. Data sifting.
7. What is the significance level of a hypothesis test?
a.
b.
c.
d.
e.
The probability that the null hypothesis is false.
The probability that the null hypothesis is true.
The probability of rejecting the null hypothesis when, in fact, the null hypothesis is false.
The probability of rejecting the null hypothesis when, in fact, the null hypothesis is true.
It is always 0.05
8. Which of the following is a true statement about the Central Limit Theorem for sample means?
a. All of the following statements are true about the Central Limit Theorem for sample means
b. If the sample size is large, the normal distribution can still be used to perform statistical inference.
c. If conditions are met, the mean of the sampling distribution is equal to the population mean.
d. The Central Limit Theorem helps us find probabilities for sample means when those means are based on a random
sample from a population.
e. None of the statements are true.
9. With a two-tailed test, if the test statistic is far from zero, will the p-value be large or small?
a.
b.
c.
d.
e.
The p-value will be small because a test statistic far from zero is indicative of a very likely event.
The p-value will be small because a test statistic far from zero is indicative of a very unlikely event.
The p-value will be large because a test statistic far from zero is indicative of a very unlikely event.
The p-value will be large because a test statistic far from zero is indicative of a very likely event.
It is impossible to say without knowing the value of the test statistic.
10. A researcher compares men and women on 200 different variables using a two- sample t-test. He sets the level of
significance to .05 and then carries out 200 independent t-tests (one for each variable) on these data. If, for each test, the
null hypothesis actually is true, about how many "statistically significant" results will be produced?
a. 0
b. 5
c. 10
d. It’s impossible to know about how many "statistically significant" results will be produced.
e. None of the above.
11. Which of the following is not true about the alternative hypothesis?
a.
b.
c.
d.
e.
It is usually a statement that the researcher hopes to demonstrate is true.
It is sometimes called the research hypothesis.
Like the null hypothesis, it is always a statement about a population parameter.
It is assumed to be true based on the sample results.
None of the above are true.
12. A researcher carried out a hypothesis test using a left-tailed alternative hypothesis. Which of the following z-scores is
associated with the smallest p-value?
a.
b.
c.
d.
e.
z = 1.92
z = -3.44
z = -1.92
z = 3.44
z=0
13. In hypothesis testing of a population mean, what does a negative test statistic mean?
a.
b.
c.
d.
e.
The sampling conditions were not met.
The test was done incorrectly.
The sample mean was less than the assumed population mean in the null hypothesis.
The assumed population mean in the null hypothesis was less than the sample mean.
The sample mean was equal to the population mean.
14. What does the term “power” refer to in hypothesis testing?
a.
b.
c.
d.
e.
The probability of rejecting the null hypothesis when the null hypothesis is false.
The probability of rejecting the null hypothesis when the null hypothesis is true.
The probability of failing to reject the null hypothesis when the null hypothesis is true.
The probability of failing to reject the null hypothesis when the null hypothesis is false.
The probability of failing to reject the null hypothesis when the alternative hypothesis is false.
15. Suppose it was reported on the news that a recent study concluded that the probability that you will get brain cancer if you
use a cell phone more than doubled from 1 in 400,000 to 1 in 200,000. Choose the statement that best summarizes the
significance of this result.
a. Many would say that this result has both clinical and statistical significance because the probability more than doubled
and this result could have a significant impact on lives.
b. Many would say that this result does not have clinical or statistical significance because the probabilities are so small
that they are meaningless.
c. Although this result may have clinical significance, it does not have statistical significance since the probability that you
will get brain cancer if you use cell phone is still so small that it is unlikely to have a meaningful affect on lives.
d. Although this result may have statistical significance, it does not have clinical significance since the probability that you
will get brain cancer if you use cell phone is still so small that it is unlikely to have a meaningful affect on lives.
e. It’s impossible to make a conclusion without knowing the p-value from the analysis.
Use the following information to answer questions (16) – (18). A sprint duathlon consists of a 5 km run, a 20 km bike
ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67
hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group
was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.
16. In this example, the numerical values of 1.62 hours and 0.40 hours are __________.
a.
b.
c.
d.
estimates
statistics
parameters
unbiased estimators
17. Suppose we were to make a histogram of the finishing times of the 30 participants in the 40-44 age group. Would the
histogram be a display of the population distribution, the distribution of sample, or the sampling distribution of means?
a.
b.
c.
d.
Population distribution
Distribution of a sample
Sampling distribution of means
None of the above.
18. Suppose the process of taking random samples of size 30 from the 40-44 age group is repeated 500 times and a histogram
of the 500 sample means is created. Which statement best describes the shape of the histogram?
a.
b.
c.
d.
The histogram will be roughly symmetrical.
The histogram will be unimodal.
The histogram will be roughly bell-shaped
All of the above statements are true.
19. What is the reason the significance level is not made arbitrarily small?
a.
b.
c.
d.
e.
Doing so would decrease the probability that the study would be replicable.
Doing so decreases the probability of correctly rejecting the null hypothesis.
Doing so would require the sample size to be too large.
Doing so increases the power of the test.
Doing so increases the probability of correctly rejecting the null hypothesis.
20. What is the difference between the t-distribution and the standard normal distribution?
a.
b.
c.
d.
e.
The t-distribution has thicker tails than the standard normal distribution.
The t-distribution is more “bell-shaped.”
The mean of the t-distribution is 0.
The t-distribution is unimodial and symmetric.
The t-distribution has thinner tails than the standard normal distribution.
21. Hypotheses are always statements about which of the following?
a.
b.
c.
d.
e.
Estimators.
Sample statistics.
Sample size.
Population parameters.
Sample parameters.
22. A confidence interval communicates an estimate of the mean and also which of the following?
a.
b.
c.
d.
e.
The sample size that was used to make the estimate.
An estimate of the standard deviation.
A measure of one’s uncertainty in the estimate.
The standard deviation of the population.
None of the above.
Math 140
Exam 3B – Written
Name______________________________________________
CSUN ID___________________________________________
GPA’s from one hundred randomly selected sample of CSUN students were collected (assume independence). The technician in
charge of records claimed that the population mean GPA for all CSUN students is 2.45. Test the technician’s claim using a level
of significance of 0.01. (Each problem is worth 5 points)
1. State the null and alternative hypothesis USING THE CORRECT NOTATION.
2. Which test statistic would you use here and why?
3. Verify that the conditions for the test are met.
4. Suppose Statcruch gave you a p-value of 0.049.
a) What does this p-value mean in the context of the problem?
b) State your results and conclusion of the hypothesis test in the context of the problem.
5. Suppose you computed a 95% confidence interval of [2.40, 2.85]. Explain what being 95% confident means in the context of
the problem.