Aw, nuts! A company claims that each batch of its deluxe mixed nuts
contains cashews, almonds, macadamia nuts, and 8% Brazil nuts. To test this claim, a quality-control inspector takes a random sample of nuts from the latest batch. The table displays the sample data.
a. State appropriate hypotheses for performing a test of the company’s claim.
b. Calculate the expected count for each type of nut.
c. Calculate the value of the chi-square test statistic.
|Type of nuts||Count||Frequency||Expected|
Part (c) The chi-square test statistic
|Type of nut||Count||Frequency|
The null and alternative hypotheses:
Expected count will be:
|Type of nuts||Count||Frequency||Expected|
|Type of nuts||Observed||Expected||% of chisq|
What’s your sign? The University of Chicago’s General Social Survey (GSS) is the nation’s most important social science sample survey. For reasons known only to social scientists, the GSS regularly asks a random sample of people their astrological sign. Here are the counts of responses from a recent GSS of people:
If births are spread uniformly across the year, we expect all signs to be equally likely. Do these data provide convincing evidence at the significance level that all signs are not equally likely?
Do students who read more books for pleasure tend to earn higher grades in English? The boxplots show data from a simple random sample of students at a large high school. Students were classified as light readers if they read fewer than books for pleasure per year. Otherwise, they were classified as heavy readers. Each student’s average English grade for the previous two
marking periods was converted to a GPA scale, where
Reading and grades (10.2) Summary statistics for the two groups from Minitab are provided.
a. Explain why it is acceptable to use two-sample procedures in this setting.
b. Construct and interpret a confidence interval for the difference in the mean English grade for light and heavy readers.
c. Does the interval in part (b) provide convincing evidence that reading more causes a difference in students’ English grades? Justify your answer.
Opinions about the death penalty The General Social Survey (GSS) asked separate random samples of people with only a high school degree and people with a bachelor’s degree, “Do you favor or oppose the death penalty for persons convicted of murder?” Of the people with only a high school degree, favored the death penalty, while of the people with a bachelor’s degree favored the death penalty. We can test the hypothesis of “no difference” in support for the death penalty among people in these educational categories in two ways: with a two-sample z test or with a chi-square test.
a. State appropriate hypotheses for a chi-square test.
b. Here is Minitab output for a chi-square test. Interpret the P-value. What conclusion would you draw?
c. Here is Minitab output for a two-sample z test. Explain how these results are consistent with the test in part (a).
Cocaine addicts need cocaine to feel any pleasure, so perhaps giving them an antidepressant drug will help. A -year study with chronic cocaine users compared an antidepressant drug called desipramine with lithium (a standard drug to treat cocaine addiction) and a placebo. One-third of the subjects were randomly assigned to receive each treatment. At the end of the study, researchers recorded whether or not the subjects relapsed. Which of the following conditions must be satisfied to perform the appropriate chi-square test using the data from this study?
I. The population distribution is approximately Normal.
II. The treatments were randomly assigned.
III. The observed counts are all at least .
a. I only
b. II only
c. III only
d. II and III
e. I, II, and III
Fruit flies Biologists wish to mate pairs of fruit flies having genetic makeup RrCc, indicating that each has one dominant gene (R) and one recessive gene (r) for eye color, along with one dominant (C) and one recessive (c) gene for wing type. Each offspring will receive one gene for each of the two traits from each parent, so the biologists predict that the following phenotypes should occur in a ratio of
Assume that the conditions for inference are met. Carry out a test at the significance level of the proposed genetic model.
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