Nondigestible oligosaccharides are known to stimulate calcium absorption in rats. A double-blind, randomized experiment investigated whether the consumption of oligofructose similarly stimulates calcium absorption in healthy male adolescents 14 to 16 years old. The subjects took a pill for nine days and had their calcium absorption tested on the last day. The experiment was repeated three weeks later. Some subjects received the oligofructose pill in the first round and then a pill containing sucrose (which served as a control). The order was switched for the remaining subjects. Here are the fractional calcium absorption data (in percent of intake) for 11 subjects:

Subject	1	2	3	4	5	6	7	8	9	10	11
Control	78.4	76.6	57.4	51.5	49.0	46.6	44.2	42.9	37.2	34.1	24.6
Oligofructose	62.0	95.1	46.5	49.4	89.7	43.8	50.3	51.6	66.6	52.7	54.0

(a) Examine the data. Is it reasonable to use the t procedures?

(b) Do the data support the hypothesis that oligofructose facilitates calcium absorption? Use significance level a 5%.

Hallux abducto valgus (call it HAY) is a deformation of the big toe that often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 38 consecutive patients under the age of 21 who came to a medical center for surgery to correct HAY. The angle is a measure of the seriousness of the deformity. Here are the data:

28 32 25 34 38 26 25 18 30 26 28 13 20

21 17 16 21 23 14 32 25 21 22 20 18 26

16 30 30 20 50 25 26 28 31 38 32 21

It is reasonable to regard these patients as a random sample of young patients who require HAY surgery. Carry out the Solve and Conclude steps of a 95% confidence interval for the mean HAY angle in the population of all such patients.

Use Table C or software to find

(a) the critical value for a one-sided test (in the greater than direction) with level a= 0.05 based on the t(5) distribution.

(b) the critical value for a 98% confidence interval based on the t(21) distribution.

Students in a physiology lab collected 50 wood lice ("pill bugs") from the university grounds. Regard these as a random sample of wood lice on Regard these as a random sample of wood lice on the university grounds. Here are the lengths in millimeters:

11.0 11.1 10.1 10.8 9.2 9.0 11.0 9.5 8.0 14.6

9.1 9.7 12.0 12.5 13.1 11.7 8.1 8.7 11.9 10.3

8.1 8.3 8.2 12.1 12.3 10.9 8.9 7.5 9.0 8.2

8.3 9.0 7.9 10.5 10.0 9.8 8.9 11.0 11.0 10.9

11.0 11.5 11.0 13.9 9.3 8.5 10.2 8.3 9.1 7.0

Verify that there are no outliers in the data. What is a 95% confidence interval for the mean body length in this population?

The alcohol content of wine depends on the grape variety, the way in which the wine is produced from the grapes, the weather, and other influences. Here are data on the percent of alcohol in wine produced from the same grape variety in the same year by 48 winemakers in the same region of Italy:

12.86 12.88 12.81 12.70 12.51 12.60 12.25 12.53 13.49 12.84

12.93 13.36 13.52 13.62 12.25 13.16 13.88 12.87 13.32 13.08

13.50 12.79 13.11 13.23 12.58 13.17 13.84 12.45 14.34 13.48

12.36 13.69 12.85 12.96 13.78 13.73 13.45 12.82 13.58 13.40

12.20 12.77 14.16 13.71 13.40 13.27 13.17 14.13

(a) Make a histogram of the data, using class width 0.25. The shape of the distribution is a bit irregular, but there are no outliers or strong skewness. There is no reason to avoid use oft procedures for n = 48.

(b) Give a 95% confidence interval for the mean alcohol content of wine of this type. (c) Based on your confidence interval, is the mean alcohol content significantly different at the a = 0.05 level from 12%? From 13%?

Sharks. Great white sharks are big and hungry. Here are the lengths in feet of 44 great whites:

(a) Examine these data for shape, center, spread, and outliers. The distribution is reasonably Normal except for one outlier in each direction. Because these are not extreme and preserve the symmetry of the distribution, use of the t procedures is safe with 44 observations.

(b) Give a 95% confidence interval for the mean length of great white sharks. Based on this interval, is there significant evidence at the 5% level to reject the claim "Great white sharks average 20 feet in length"?

(c) Before accepting the conclusions of (b), you need more information about the data. What would you like to know?

Because the t procedures are robust, the most important condition for their safe use is that

(a) the population standard deviation a- is known.

(b) the population distribution is exactly Normal.

(c) the data can be regarded as an SRS from the population.

Which of these settings does not allow use of a matched pairs t procedure?

(a) You interview both the husband and the wife in 64 married couples and ask each about their ideal number of children.

(b) You interview a sample of 64 unmarried male students and another sample of 64 unmarried female students and ask each about their ideal number of children.

(c) You interview 64 female students in their freshman year and again in their senior year and ask each about their ideal number of children.

Which of the following would be most worrisome for the validity of the confidence interval you calculated in the previous exercise?

(a) The presence of a clear outlier in the raw data

(b) A mild skew in the stemplot of the raw data

(c) Not knowing the population standard deviation s

Data on the blood cholesterol levels of 24 rats in mg/di give x = 85 ands = 12. A 95% confidence interval for the mean blood cholesterol of rats under this condition is

(a) 78.7 to91.3.

(b) 79.9 to 90. l.

(c) 80.2 to 89.8.

You have an SRS of 15 observations from a Normally distributed population. What critical value would you use to obtain a 98% confidence interval for the mean u of the population?

(a) 2.326

(b) 2.602

(c) 2.624

You are testing Ho: u = 240 against Ha: u not equal to 240 based on an SRS of 16 observations from a Normal population. The t statistic is t = - 2.112. The P-value for this test

(a) falls between 0.025 and 0.05.

(b) falls between 0.05 and 0.10.

(c) is greater than 0.50.

The P-value for the statistic in the previous exercise

(a) falls between 0.01 and 0.02.

(b) falls between 0.02 and 0.04.

(c) is greater than 0.25.

You are testing Ho: u = 10 against Ha: u smaller than 10 based on an SRS of 20 observations from a Normal population. The t statistic is t = -2.25. The degrees of freedom for this statistic are

(a) 19.

(b) 20.

(c) 21.