Question 13.14

Biologists studying the healing of skin wounds measured the rate at which new cells closed a razor cut made in the skin of an anesthetized newt. Here are data from 18 newts, measured in micrometers (millionths of a meter per hour:

29 27 34 40 22 28 14 35 26

35 12 30 23 18 11 22 23 33

1. Make a stemplot of the healing rates (split the stems). It is difficult to assess Normality from 18 observations, but look for outliers or extreme skewness. What do you find?
2. Scientists usually assume that animal subjects are SRSs from their species or genetic type. Treat these newts as an SRS and suppose you know that the standard deviation of healing rates for this species of newt is 8 micrometers per hour. Give a 90% confidence interval for the mean healing rate for the species.
3. A friend who knows almost no statistics uses the formula \[\overline{x}\pm 1.96\sigma /\sqrt{N}\] in a biology lab manual to get a 95% confidence interval for the mean. Is her interval wider or narrower than yours? Explain to her why it makes sense that higher confidence changes the length of the interval.

Question 13.28

A Gallup Poll in December 2000 asked, "Do you think this country would be governed better or governed worse if more women were in political office?" Of the 1026 adults in the sample, 57% said "better." Gallup added, "For results based on the total sample of National Adults, one can say with 95% confidence that the margin of sampling error is 3 percentage points." Explain to someone who knows no statistics what the phrase "95% confidence" means here.

Question 14.28

Sulfur compounds cause "off-odors" in wine, so winemakers want to know the odor threshold, the lowest concentration of a compound that the human nose can detect. The odor threshold for dimethyl sulfide (DMS) in trained wine tasters is about 25 micrograms per liter of wine (g/l). The untrained noses of consumers may be less sensitive, however. Here are the DMS odor thresholds for 10 untrained students:

31 31 43 36 23 34 32 30 20 24

Assume that the odor threshold for untrained noses is Normal with = 7g/l. Is there evidence that the mean threshold for untrained taster is greater than 25 g/l?

Question 14.42

Does the destruction of large trees in a windstorm change forests in any important way? Here is the conclusion of a study that found that the answer is no:

We found surprisingly little divergence between treefall areas and adjacent control areas in the richness of woody plants (P = 0.62), in total stem densities (P = 0.98), or in population size or structure for any individual shrub or tree species.

The two P values refer to null hypothesis that say "no change" in measurements between treefall and control areas. Explain clearly why these values provide no evidence of change.

Question II .8

The mean blood cholesterol level for all men aged 20 – 34 years is \[\mu =188mg/dl\] . We suspect that the mean for cross-country runners is lower. State hypotheses, use the information in exercise II.6 (below) to find the test statistic, and five the P-value. Is the result significant at the = 0.10 level? At = 0.05? At = 0.01?

II.6 The distribution of blood cholesterol level in the population of young men aged 20 -34 years is close to Normal with standard deviation of = 41 milligrams per deciliter (mg/dl). You measure the blood cholesterol of 14 cross country runners. The mean level is \[\overline{x}\] = 172 mg/dl. Assuming that is the same as in the general population, give a 90% confidence interval for the mean level among cross-country runners.

Question 15.26

A New York Times/CBS News poll asked the question "Do you favor an amendment to the Constitution that would permit organized prayer in public schools?" Sixty-six percent of the sample answered "Yes." The article describing the poll says that it "is based on telephone interview conducted from Sept. 13 to Sept. 18 with 1664 adults around the United States, excluding Alaska and Hawaii….the telephone numbers were formed by random digits, thus permitting access to both listed and unlisted residential numbers." The article gives the margin of error as 3 percentage points. Opinion polls customarily announce margins of error for 95% confidence, so we are 95% confident that the percent of all adults who favor prayer in the schools lies in the interval 66% ± 3%.

The new article goes on to say: "the theoretical errors do not take into account a margin of additional error resulting from the various practical difficulties in taking any survey of public opinion." List some of the "practical difficulties" that may cause errors in addition to the 3% margin of error. Pay particular attention to the news article’s description of the sampling method.

Price: $21.61

Solution: The downloadable solution consists of 8 pages, 1361 words and 2 charts.
Deliverable: Word Document