1. _______________ is the process of estimating properties of a population from a sample.
a. Sampling
b. Statistical inference
c. Observational study
d. Sampling Distribution
2. Imagine that there are 100 different researchers each studying the sleeping habits of college freshmen. Each researcher takes a random sample of size 50 from the same population of freshmen. Each researcher is trying to estimate the mean hours of sleep that freshmen get at night, and each one constructs a 95% confidence interval for the mean. How many of these 100 confidence intervals will NOT capture the true mean?
a. All will contain the true mean
b. Exactly 5 will not contain the true mean
c. Approximately 5 will not contain the true mean
d. Exactly 95 will not contain the true mean
e. Approximately 95 will not contain the true mean
3. Two researchers are going to take a sample of data from the same population of physics students. Researcher A will select a random sample of students from among all students taking physics. Researcher B's sample will consist only of the students in her class. Both researchers will construct a 95% confidence interval for the mean score on the physics final exam using their own sample data. Which researcher's method has a 95% chance of capturing the true mean of the population of all students taking physics?
a. Both methods have a 95% chance of capturing the true mean
b. Researcher A
c. Research B
d. Neither
4. Some methods may be used to make a confidence interval wider or narrower. Check the following methods that would decrease the width of a confidence interval for a mean, if all else stays the same. For each choice you select, explain why that would decrease the confidence interval.
a. Increase the sample size.
b. decrease the sample size.
c. increase the level of confidence.
d. decrease the level of confidence.
5. The Gallup Organization typically uses about 1,000 people for their surveys and 95% confidence levels. Assuming Gallup is conducting a survey involving YES/NO data, what is the maximum margin of error they would have with this sample size? Explain your reasoning.
6. A 95% confidence interval for a mean indicates that:
About 95% of the intervals constructed using this process based on samples from this population will include the population mean
About 95% of the time the interval will include the sample mean
About 95% of the population will be covered by the interval
7. A statistical test of hypotheses correctly carried out proves one of the two hypotheses, either the null or the alternative one. Is this True or False? Explain the reason.
8. What is the role of the test statistic in hypothesis testing?
9. You conduct a hypothesis to determine if a certain training regimen has a positive impact on runners' speeds. The mean mile time for the runners before implementing the training regimen was 7.45 minutes.
The statement below is not the correct symbolic statement of the null hypothesis. Explain what is wrong with it and why it doesn't make sense the way it's stated.
H0: X ¯ = 7.45.
Suppose the test statistic has a standard normal distribution. Which value of the statistic would give greater evidence against the null hypothesis, Z= -2.3 or Z = 1.7? Explain.
10. Why do we reject the null hypothesis when the p-value is small? Explain as if to someone unfamiliar with statistics.
11. Why do we divide by the standard error when computing a test statistic?