## Instructions

This homework is due on Tuesday, October 10th at 2pm (the start of class). Please turn in all your work. This homework covers sign tests and variations, and the start of 2x2 contingency tables.

• Calculations by hand: Throughout this homework, and beyond, “by hand” means either (1) you utilize quantile/distribution tables, and/or Gaussian approximations, as appropriate, and otherwise do all of your calculations with pen and paper (and a calculator); or (2) you write code, say in R, building up all of the steps yourself, i.e., not using a library function that automates the entire procedure (see next bullet).

• Using a software library: Through this the homework, and beyond, “using a software library” means you can feed your data into a built-in function, like t.test and binom.test in R, and interpret the output as appropriate. Be sure to provide details on the library you used, how you used it, what the output was, and what it means.

### Problem 1: Weight Loss (17 pts)

Six students went on a diet in an attempt to lose weight, with the following results:

weights <- data.frame(
name=c("Abdul", "Ed", "Jim", "Max", "Phil", "Ray"),
before=c(174, 191, 188, 182, 201, 188),
after=c(165, 186, 183, 178, 203, 181))

Is the diet an effective means of losing weight?

1. (9 pts) Perform the test “by hand”.
2. (8 pts) Perform the test “using a software library”.

### Problem 2: Concrete (16 pts)

Two different additives were compared to see which one is better for improving the durability of concrete. One hundred small batches of concrete were mixed under various conditions and, during the mixing, each batch was divided into two parts. One part received additive A and the other part received additive B.

After the concrete hardened, the two parts in each batch were crushed against each other, and an observer determined which part appeared to be the most durable. In 77 cases the concrete with additive A was rated more durable, whereas in 23 cases the concrete with additive B was rated more durable. Is there a significant difference between the effects of the two additives?

1. (8 pts) Perform the test “by hand”.
2. (8 pts) Perform the test “using a software library”.

### Problem 3: Foreign Policy (17 pts)

One hundred thirty-five citizens were selected at random and were asked to state their opinion regarding U.S. foreign policy. Forty-three were opposed to the foreign policy. After several weeks, during which they received an informative newsletter, they were again asked their opinion; 37 were opposed, and 30 of the 37 were persons who originally were not opposed to the U.S. foreign policy. Is the change in numbers of people opposed to the U.S. foreign policy significant?

1. (9 pts) Perform the test “by hand”.
2. (8 pts) Perform the test “using a software library”.

### Problem 4: Automobile fatality (16 pts)

In a certain city the mortality rate per 100,000 citizens due to automobile accidents for each of the last 15 years was:

mortality <- c(17.3, 17.9, 18.4, 18.1, 18.3, 19.6, 18.6, 19.2, 17.7, 20.0, 19.0, 18.8, 19.3, 20.2, 19.9)

Is there any basis for the statement that the mortality is increasing?

1. (8 pts) Perform the test “by hand”.
2. (8 pts) Perform the test “using a software library”.

### Problem 5: Toothpaste (17 pts)

One hundred men and one hundred women were asked to try a new toothpaste and to state whether they liked or did not like the new taste. Thirty-two men and twenty-six women said they did not like the new taste. Does this indicate a difference in preferences between men and women in general?

1. (9 pts) Perform the test “by hand”.
2. (8 pts) Perform the test “using a software library”.

### Problem 6: Flowers (17 pts)

A florist maintains that certain venues have a preference for a certain type of flower to decorate for weddings. In order to test this claim, she had 10 available decorative gardenias and 10 available decorative tulips. Venue A had 8 weddings on the list and Venue B had 12 weddings on its list. Venue A used gardenias on 5 different occasions. Does this indicate that there is a significant difference in the use of gardenias across venues?

1. (9 pts) Perform the test “by hand”.
2. (8 pts) Perform the test “using a software library”.