Here’s your final reading assignment. Read Section 6.2 in your textbook (omitting Section 6.2.4) and answer the following questions by noon, Monday, April 16th. Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

1. Conducting a two-sample t-test requires that the underlying populations for both samples are normal. What are two methods we’ve seen for checking this normality assumption?
2. Suppose you recruit 10 Vanderbilt undergraduates at random to sample the coffee at Starbucks and Panera, rating each store’s coffee on a scale of 1 to 5. The average of the differences in the 10 pairs of ratings is 0.7 in favor of Starbucks, with a standard deviation of 0.5. Is this sufficient evidence to conclude that all Vanderbilt students prefer Starbucks coffee to Panera coffee? (Assume that the underlying populations here are normal.)
3. What’s one question you have about the reading?

Here’s your penultimate reading assignment. Read Section 6.1 in your textbook and answer the following questions by 8 a.m., Friday, April 13th. Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

1. Suppose that a random sample of 10 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let μ denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval is (7.5, 9.4). If the sample size had been 50 instead of 10 but the sample mean and sample standard deviation were the same, would the 95% confidence interval constructed from this larger sample have been narrower or wider than the given interval from the smaller sample? Explain your reasoning.
2. Suppose a random sample of 10 Vanderbilt undergraduates is found to have an average height of 67 inches and a sample standard deviation of 3 inches. Construct a 95% confidence interval for the average height of the population of all Vanderbilt undergraduates. What assumptions are required to construct this confidence interval?
3. What’s one question you have about the reading?

Here’s your next reading assignment. Read Section 5.4 in your textbook and “Ending the Infographic Plague” by Megan McArdle and answer the following questions by 8 a.m., Friday, April 6th. Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

1. The authors suggest that if a sample size is less than 10% of the population size, we can treat the observations in the sample as independent. Why is that reasonable?
2. When H₀: p₁ = p₂, why does it make sense to use the pooled estimate of the sample proportion instead of the two individual sample means?
3. Given McArdle’s concerns about infographics, what are one or two things you can do when designing your application project infographic to make it an effective one?
4. What’s one question you have about the reading?

Here’s your next reading assignment. Read Section 5.3 in your textbook and answer the following questions by 8 a.m., Wednesday, April 4th. Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

1. Which of p and “hat p” (seen in the margin on page 203) is a random variable?
2. In a study designed to investigate whether certain detonators used with explosives in coal mining meet the requirement that more than 90% will ignite the explosive when charged, it is found that 185 of 200 detonators function properly. Is this convincing evidence that this type of detonators work as they should?
3. If you want to determine the smallest sample size n so that the margin of error of a point estimate for a population proportion is no larger than m = 0.04, do you need to know the size of the population? Why or why not?
4. What is one question you have about the reading?

Here’s your next reading assignment. Read Sections 5.1-5.2 in your textbook and answer the following questions by 8 a.m., Monday, April 2nd. Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

1. Suppose you’ve developed a vehicle back-up camera and you suspect that it will help drivers parallel park more quickly. You have twelve volunteers parallel park an SUV without the camera, and then you have a different twelve volunteers parallel park the same SUV while using the camera. You compare the time it takes each group of volunteers to park the SUV. Are these samples paired or unpaired? Explain your answer.
2. Suppose that the drinking water in two cities, Phoenix and Las Vegas, is sampled and tested for arsenic. The average arsenic level in the 50 Phoenix samples was 12.5 parts per billion (ppb) with a standard deviation of 7.63. The average arsenic level in the 50 Las Vegas samples was 15.4 ppb with a standard deviation of 15.3. Conduct a hypothesis test using these data to determine if the arsenic levels in these two cities are different.
3. Answer the question posed in Exercise 5.14 on page 201.
4. What question do you have about the reading?

Here’s your next reading assignment. Read Sections 7.1-7.2 in your textbook and answer the following questions by 8 a.m., Wednesday, March 21st. Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

1. Compute the residual for the observation (95.5, 94.0), the one marked with a triangle on Figure 7.6, using the linear model given in Equation 7.1.
2. Take a look at the residual plot in part (a) of question 7.2 on page 296. Imagine the x-y scatterplot for these data. Based on the residual plot, what can you about the scatterplot?
3. Assuming that the line of best fit for the possum data seen in Figure 7.4 is indeed y = 41 + 0.59x, what does the number 0.59 tell you about possums?
4. What’s one question you have about the reading?

Here’s your next reading assignment. Read Sections 4.3.4-4.4 in your textbook and answer the following questions by 8 a.m., Wednesday, March 14th. (Yes, that’s Pi Day. No, I don’t think that’s the coolest thing ever.) Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

1. Consider the hypothesis test H₀: μ = 100 vs. H_A: μ < 100. Suppose the p-value for this test using a particular sample turns out to be p=0.04. What probability does this p-value represent? Be as specific as possible.
2. Example 4.38 on page 167 provides a justification for the advice to never change a two-sided test to a one-sided test after observing the data. Do you accept this justification? Why or why not?
3. In the example discussed in class on Monday, the hypothesis test H₀: μ = 494 vs. H_A: μ > 494 was conducted and found to have a p-value of p=.2743. Under what conditions would you be okay to reject the null hypothesis given this p-value?
4. What’s one question you have about the reading?

Here’s your next reading assignment. Read Sections 4.3.1-4.3.3 in your textbook and answer the following questions by 8 a.m., Friday, March 2nd. Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

1. Water samples are taken from water used for cooling as it is being discharged
   from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150 degrees Fahrenheit, there will be no negative effects on the river’s ecosystem. To investigate whether the plan is in compliance with the regulations that prohibit a mean discharge water temperature above 150 degrees, 50 water samples will be taken at randomly selected times, and the temperatures of each sample recorded. Identify an appropriate null and alternative hypothesis for this test, and justify your answer.
2. Suppose, in the context of the previous context, the average temperature for the 50 water samples collected was 152 degrees. Why is it too simple just to say that since 152 is greater than 150, the power power plant discharge temperature is higher than it should be?
3. What’s one question you have about the reading?

Here’s your next reading assignment. Read Sections 4.1 and 4.2 in your textbook and answer the following questions by 8 a.m., Monday, February 27th. Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

1. Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let μ denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval is (7.5, 9.4). Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning.
2. Suppose a random sample of 30 Vanderbilt undergraduates is found to have an average height of 67 inches and a sample standard deviation of 3 inches. Construct a 95% confidence interval for the average height of the population of all Vanderbilt undergraduates and interpret its meaning.
3. What’s one question you have about the reading?

Here’s your next reading assignment. Read this short article on geostatistics by 8 a.m., Monday, February 20th. Be sure to login (using the link near the bottom of the sidebar) to the blog before leaving your answers in the comment section below.

1. In this course, we’ve focused on the difference between a population and a sample drawn from that population. In the example in the article about rainfall in Sweden, what is the population and what is the sample?
2. Suppose that in 1993 you selected a citizen of Belarus at random and tested the milk in his or her refrigerator for radiocesium. What are some reasons the level of radiocesium might vary from citizen to citizen?  Which of these reasons would be relatively easy to model mathematically?
3. What’s one question you have about the reading?