Download Chapters 20

1. If σ is 5.3 based on past research, and you want to construct a 97% confidence interval for μx, what
value for Z would you use?
2. Using a random sample of 2,000 students, you compute a 95% confidence interval to estimate the mean
calories consumed by eighth graders. You decide to compute another 95% confidence interval using a
different sample of eighth graders, this time only 1000 students. What, if any, change would you expect
from the first to the second confidence interval?
3. If a p-value is statistically significant, this means that:
4. A one-sided, lower tail hypothesis test with an α = .05, could be evaluated using the lower bound of an
80% confidence interval?
5. Random sampling is important in studies where you will be calculating p-values.
6. It is believed that a population of one-eyed fish has a normal distribution with a mean of 3.4 kg and a
standard deviation of 0.8 kg. A simple random sample of 30 such fish is taken. The mean of this sample is
3 kg. Which calculator statement would find the p-value of a hypothesis test, if Ha: µ < 3.4?
7. You conduct a one-sided, upper tail test of Ho at α = 0.01. What is the critical z-value for this test?
8. You conduct a hypothesis test and find a p-value of 0.025. Which of the following is true?
9. If a significance test has you reject Ho at the 0.05 level of significance, which of the following is(are)
true?
I. Ho can be rejected at the 0.10 level of significance.
II Ha can be rejected at the 0.05 level of significance.
III Ho can be rejected at the 0.01 level of significance.
10. Suppose we have a hypothesized population mean of µ = 50, and we use our sample data to construct
a 98% confidence interval of (48, 54). Which of these statements is true if our alternative hypothesis is µ ≠
50?
11. HairBuilders Inc. claims that its product can cure male pattern baldness. A “friend of mine” tests the
company’s claim. If “my friend” makes a Type I error in his evaluation of the claim, which of the
following would be true?
12. A market claims the average weight of a package of hamburger in its meat department is one pound,
with a standard deviation of 0.18 pounds. A manager decides to test Ho: µ = 1 against the two-sided
alternative Ha: µ ≠ 1. He decides to reject Ho if the mean of a sample of 35 packages differs from µ by
more than 1.5 standard deviations. What is the probability of a Type I error?
13. Management of El Burrito decides that if the burritos are larger than the standard weight of 1.2
pounds, drink sizes will have to be reduced to compensate for the loss of profits. For a one-sided
hypothesis test where Ho: µ = 1.2 lb, Ha: µ > 1.2 lb, and α = 0.01, which of these statements represents a
Type II error?
14. What critical t-value would you need to have for a 90% confidence interval for μx based on a sample
of size 22?
15. Compute the p-value for a hypothesis test where Ho: µ = 14.75 and Ha: µ ≠ 14.75 if a random sample
of 23 yielded sx = 2.33, and X = 15.5. Also give a conclusion for a test where α = 0.05.
16. Which of the following scenarios is not a matched pairs situation?
17. The following scenario can be analyzed using a matched pair procedure: Thirty couples applying for
marriage licenses are asked to give their ages. The researcher wants to know if husbands trend to be older
than their wives.
18. Which of the following statements about matched pairs analysis are true?
I. In a matched pairs analysis, you use a single-sample procedure. The sample is made up of the
differences between pairs of observations.
II. In matched pairs analysis, the two original samples are said to be dependent on each other.
III. In a matched pairs analysis each of the two original samples is analyzed separately before
comparing their means.
19. High Voltage Inc., a light bulb manufacturer wants to know if there is a difference in mean life span of
their bulbs and that of a competitor. The company has collected data for a matched pairs analysis,
calculated the differences in the pairs of data to make one set of values, and set up the test
Ho: µ(High Volt – Competitor) = 0
Ha: µ(High Volt – Competitor) ≠ 0
What conclusion can be drawn if the p-value = 0.001 and α = 0.05?
20. We draw two independent simple random samples from two distinct approximately normally
distributed populations. The means and the standard deviations of the populations are unknown. We are
interested in comparing the two populations to see if their means are the same. Which of the following
procedures could we use to get this information?
21. Suppose you want to know if comedy movies tend to be shorter than action movies. You take a
random sample of five movies from each genre, and compare the average lengths of both samples. What
would you need to know if you wanted to use a two sample t procedure here?
22. Which of the following statements about pooling is(are) true?
I. In statistics, to pool is to create an estimate of a common variance for two samples.
II. All things being equal, pooling gives a smaller estimate of the standard deviation than either of
the two individual standard deviations
III. Pooling can be done in the rare occasions when the population sizes can be assumed to be
equal.
IV. You can use pooling when the standard deviations of the samples are the same.
23. You are interested in determining whether there is a difference in people’s preferences for orange or
pink food. To see if there is a difference you make a large batch of vanilla pudding and dye one half pink
and the other half orange. You ask 132 random people to sample each color, and you randomize which
color they sample first. You record the proportion, p-hat, of people who choose pink over orange. What
would be an appropriate null and alternative hypothesis be, if p = the proportion of people choosing pink
over orange?
24. A random sample of 384 people in a mid-sized city revealed 112 individuals who worked at more than
one job. A second random sample of 432 workers from another mid-sized city found that 91 people
worked at more than one job. Find a 99% confidence interval for the difference between the proportions
of workers in the two cities who work at more than one job.
25. Which of the following is(are) true?
I. When generating a confidence interval or when doing a significance test with proportions, we
use the same formula for determining the standard error of the statistic.
II. If zero is in the confidence interval for the difference between two proportions we have
evidence that the two proportions could be the same.
III. When we do a significance test for the difference between two proportions, we are justified in
pooling our estimates of the populations only if the sample sizes are the same.
26. Which of the following best describes the power of a test?