A school's principal wants to know if students spend about the same amount of time on homework each night of the week. She asks a random sample of 50 students to keep track of their homework time for a week. The following table displays the average amount of time (in minutes) students reported per night. Explain carefully why it would not be appropriate to perform a chi-square test for goodness of fit using these data.

A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% brazil nuts. To test this claim, a quality-control inspector takes a random sample of 150 nuts from the latest batch. State appropriate hypotheses for performing a test of the company's claim.

Select the best answer. Which of the following is false? (a) A chi-square distribution with k degrees of freedom is more right-skewed than a chi-square distribution with k + 1 degrees of freedom. (b) A chi-square distribution never takes negative values. (c) The degrees of freedom for a chi-square test is determined by the sample size. (d)

$$P(\chi^2 > 10)$$

is greater when df = k + 1 than when df = k. (e) The area under a chi-square density curve is always equal to 1.

Kellogg's Froot Loops cereal comes in six colors: orange, yellow, purple, red, blue, and green. Charise randomly selected 120 loops and noted the color of each. Here are her data:

$$\begin{array}{lcccccc} \hline \text { Color } & \text { Orange } & \text { Yellow } & \text { Purple } & \text { Red } & \text { Blue } & \text { Green } \\ \text { Count } & 28 & 21 & 16 & 25 & 14 & 16 \\ \hline \end{array}$$

Do these data provide convincing evidence at the 5% significance level that Kellogg's Froot Loops do not contain an equal proportion of each color?

Casinos are required to verify that their games operate as advertised. American roulette wheels have 38 slots-18 red, 18 black, and 2 green. The managers of a casino record data from a random sample of 200 spins of one of their American roulette wheels. State appropriate hypotheses for performing a test of this roulette wheel.

Choose the best answer. School A has 400 students and School B has 2700 students. A local newspaper wants to compare the distributions of SAT scores for the two schools. Which of the following would be the most useful for making this comparison? (a) Back-to-back stemplots for A and B (b) A scatterplot of A versus B (c) Dotplots for A and B drawn on the same scale (d) Two relative frequency histograms of A and B drawn on the same scale (e) Two bar graphs for A and B drawn on the same scale

Statistics teacher Jason Molesky contacted Mars, Inc., to ask about the color distribution for Skittles candies. Here is an excerpt from the response he received: "The original flavor blend for the SKITTLES BITE SIZE CANDIES is lemon, lime, orange, strawberry and grape. They were chosen as a result of consumer preference test we conducted. The flavor blend is 20 percent of each flavor." How large a

$$\chi^2$$

statistic would you need to have significant evidence against the company's claim at the

$$\alpha = 0.01$$

level?

Kellogg's Froot Loops cereal comes in six fruit flavors: orange, lemon, cherry, raspberry, blueberry, and lime. Charise poured out her morning bowl of cereal and methodically counted the number of cereal pieces of each flavor. Here are her data:

$$\begin{matrix} \text{Flavor:} & \text{Orange} & \text{Lemon} & \text{Cherry} & \text{Raspberry} & \text{Blueberry} & \text{Lime}\\ \text{Count:} & \text{28} & \text{21} & \text{16} & \text{25} & \text{14} & \text{16}\\ \end{matrix}$$

Test the null hypothesis that the population of Froot Loops produced by Kellogg's contains an equal proportion of each flavor.

Aspirin prevents blood from clotting and so helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anticlotting drug named dipyridamole would be more effective for patients who had already had a stroke. Here are the data on strokes during the two years of the study:

$$\begin{array}{llcc} \text { Group } & \text { Treatment } & \text { Number of patients } & \text { Number of strokes } \\ \hline 1 & \text { Placebo } & 1649 & 250 \\ 2 & \text { Aspirin } & 1649 & 206 \\ 3 & \text { Dipyridamole } & 1654 & 211 \\ 4 & \text { Both } & 1650 & 157 \\ \hline \end{array}$$

Find the expected counts if $H_{0}$ is true, and display them in a two-way table similar to the table of observed counts.

Use your calculator's RandInt function to generate 200 digits from 0 to 9 and store them in a list. State appropriate hypotheses for a chi-square test for goodness of fit to determine whether your calculator's random number generator gives each digit an equal chance to be generated.

Which of the following statements about chi-square distributions are true? I. For all chi-square distributions, $P\left(\chi^{2} \geq 0\right)=1.$ II. A chi-square distribution with fewer than 10 degrees of freedom is roughly symmetric. III. The more degrees of freedom a chi-square distribution has, the larger the mean of the distribution. (a) I only (b) II only (c) III only (d) I and III (e) I, II, and III

A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% Brazil nuts. To test this claim, a quality-control inspector takes a random sample of 150 nuts in the latest batch. The table displays the sample data:

$$\begin{array}{lcccc} \hline \text { Type of nut } & \text { Cashew } & \text { Almond } & \text { Macadamia } & \text { Brazil } \\ \text { Count } & 83 & 29 & 20 & 18 \\ \hline \end{array}$$

Calculate the expected count for each type of nut.

Explain whether the situation is an experiment or an observational study. A caretaker at a zoo records the sleeping habits of the wildcats at the zoo for a month.

A box-shaped figure like a rectangular prism has a length of 8 inches and a width of 8 inches its volume is 512 cubic inches. What's the height of the box

A 64

B 8

C 24

D 16