The table shows prices of 50 college textbooks in a community college bookstore, rounded to the nearest dollar. Make an appropriate graph of the distribution of the data, pose a statistical question and describe the distribution.

76	19	83	45	88	70	62	84	85	87
86	37	88	45	75	83	126	56	30	33
26	88	30	30	25	89	32	48	66	47
115	36	30	60	36	140	47	82	138	50
126	66	45	107	112	12	97	96	78	60

The following table shows the first few entries for the number of hours of sleep in one night for a sample of college students. The data are stacked and coded, where $0$ represents a male student and $1$ represents a female student. What would be appropriate graphs to compare the distributions of hours of sleep in one night for male and female college students if you had the complete data set? Explain. Write a statistical question that can be answered with the complete data.

A group of 80 drivers in a large city is asked for the number of parking tickets they received in the previous month. What shape do you think this distribution will have? Explain.

The data show monthly rents for studio and one-bedroom apartments in San Francisco. Write a statistical question appropriate for these data and a brief comparison of the distribution of rents for these two types of housing units. Include appropriate graphics. (Source: Zillow)

Studio Apartments

One Bed-room Apartments

An article in the journal BMC Medicine reported on a study designed to study the effect of diet on depression. Subjects suffering from moderate to severe depression were randomly assigned to one of two groups: a diet intervention group and a social support control group. The $33$ subjects in the diet intervention group received counseling and support to adhere to a “ModiMedDiet,” based primarily on a Mediterranean diet. The $34$ subjects in the social support group participated in a “befriending” protocol, where trained personnel engaged in conversation and activities with participants. At the end of a $12$-week period, $11$ of the diet intervention group achieved remission from depression compared to $3$ of the control group.

a. Find and compare the sample percentage of remission for each group.
b. Was this a controlled experiment or an observational study? Explain.
c. Can we conclude that the diet caused a remission in depression? Why or why not?

A civil engineer wishes to measure the compressive strength of two different types of concrete. A random sample of 10 specimens of the first type yielded the following data (in psi) Type 1:

$$\begin{matrix} \text{3,250, 3,268, 4,302, 3,184, 3,266}\\ \text{3,297, 3,332, 3,502, 3,064, 3,116}\\ \end{matrix}$$

whereas a sample of 10 specimens of the second yielded the data Type 2:

$$\begin{matrix} \text{3,094, 3,106, 3,004, 3,066, 2,984,}\\ \text{3,124, 3,316, 3,212, 3,380, 3,018}\\ \end{matrix}$$

If we assume that the samples are normal with a common variance, determine (a) a 95 percent two-sided confidence interval for $\mu_{1}-\mu_{2}$, the difference in means; (b) a 95 percent one-sided upper confidence interval for $\mu_{1}-\mu_{2}$; (c) a 95 percent one-sided lower confidence interval for $\mu_{1}-\mu_{2}$.

In the following exercise, you are asked to compare three data sets. Without calculating, determine which data set has the greatest sample standard deviation and which has the least sample standard deviation. Explain your reasoning.

An instructor asks a class of 120 students how many hours they slept during the previous night. What shape do you think this distribution will have? Explain.

The blog NHS Choices (February 10, 2014) noted that “there has been increasing anecdotal evidence that vitamin C may still be useful as an anticancer medicine if used in high concentrations and given directly into the vein (intravenously).” Explain what it means that there is “increasing anecdotal evidence” that Vitamin C may be a useful anticancer medicine. How does anecdotal evidence contrast with scientific evidence? What kind of conclusions, if any, can be made from anecdotal evidence?

An article in the Journal of the Academy of Nutrition and Dietetics reported on a study of diet in subjects with moderate to severe acne. Read the excerpts from the abstract and answer the questions that follow.

Methods: Sixty-four participants (no acne, n = 32; moderate/severe acne, n = 32) were included in this study. Participants completed a 5-day food record, had blood drawn and completed a questionnaire to evaluate food-aggravated acne beliefs and acne-specific quality of life. Results: Participants with moderate/severe acne consumed greater total carbohydrate compared to participants without acne. Participants with moderate/severe acne had greater insulin compared to participants without acne. Although there were no differences between groups, 61% of participants reported food-influenced acne.

a. Was this a controlled experiment or an observational study? Explain how you know.

b. Assuming the study was properly conducted, can we conclude that higher consumption of carbohydrates causes more severe acne? Explain.

In a 2017 study designed to investigate the effects of exercise on second language learning, 40 subjects were randomly assigned to one of two conditions: an experimental group that engaged in simultaneous physical activity while learning vocabulary in a second language and a control group that learned the vocabulary in a static learning environment. Researchers found that learning second-language vocabulary while engaged in physical activity led to higher performance than learning in a static environment.

a. What features of a well-designed controlled experiment does this study have? Which features are missing?

b. Assuming that the study was properly conducted, can we conclude that the physical activity while learning caused the higher performance in learning second-language vocabulary? Explain.

The New England Journal of Medicine reported on a study of fish oil consumption in pregnant mothers and the subsequent development of asthma in their children. Read the excerpts from the abstract and answer the questions that follow: (Source: Bisgaard et al., “Fish oil–derived fatty acids in pregnancy and wheeze and asthma in offspring,” New England Journal of Medicine, vol. 375 [December 2016]: 2530–2539, doi:10.1056/NEJMoa1503734

Methods: We randomly assigned $736$ pregnant women at $24$ weeks of gestation to receive fish oil or a placebo (olive oil) daily. Neither the investigators nor the participants were aware of group assignments during follow-up for the first $3$ years of the children’s lives, after which there was a $2$-year follow-up period during which only the investigators were unaware of group assignments. Results: A total of $695$ children were included in the trial, and $95.5\%$ completed the 3-year, double-blind follow-up period. The risk of persistent wheeze or asthma in the treatment group was $16.9\%$, versus $23.7\%$ in the control group, corresponding to a relative reduction of $30.7\%$.

a. Was this a controlled experiment or an observational study? Explain how you know.
b. Assuming the study was properly conducted, can we conclude that the lower rate of asthma was caused by the mother’s consumption of fish oil?

Find the range of the data set represented by the graph.

Give an example of a data set that would be best represented in a line graph.