Skittles® Statistics teacher Jason Mole sky 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, green apple, orange, strawberry and grape. They were chosen as a result of consumer preference tests we conducted. The flavor blend is percent of each flavor.”
a. State appropriate hypotheses for a significance test of the company’s claim.
b. Find the expected counts for a random sample of candies.
c. How large a test statistic would you need to have significant evidence against the company’s claim at the α=0.05 level? At the level?
d. Create a set of observed counts for a random sample of candies that gives a value between and Show the calculation of your chi-square test statistic.
Part (b) Expected count for each flavor is
Part (c) If chi square statistic is greater than above critical values at specified level of significance then reject
The flavor blend is of each flavor.
Sample size is candies.
The null and alternative hypotheses:
To get the predicted count, multiply each frequency of flavor by As a result, the projected count is,
The degrees of freedom
For each degree of significance, various critical values will be used.
When significance level
Reject if the chi square statistic is greater than the crucial values at the selected level of significance.
The frequency of the random sample is shown in the table below:
Therefore, thevalue is between and
“Will changing the rating scale on a survey affect how people answer the question?” To find out, the group took an SRS of students from an alphabetical roster of the school’s just over students. The first students chosen were asked to rate the cafeteria food on a scale of (terrible) to (excellent). The remaining students were asked to rate the cafeteria food on a scale of (terrible) to (excellent). Here are the data:
a. Was this an observational study or an experiment? Justify your answer.
b. Explain why it would not be appropriate to perform a chi-square test in this setting.
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?
A study conducted in Charlotte, North Carolina, tested the effectiveness of three police responses to spouse abuse: advise and possibly separate the couple, issue a citation to the offender, and arrest the offender. Police officers were trained to recognize eligible cases. When presented with an eligible case, a police officer called the dispatcher, who would randomly assign one of the three available treatments to be administered. There were a total of cases in the study. Each case was classified according to whether the abuser was arrested within months of the original incident.
a. Explain the purpose of the random assignment in the design of this study.
b. State an appropriate pair of hypotheses for performing a chi-square test in this setting.
c. Assume that all the conditions for performing the test in part (b) are met. The test yields and a . Interpret this P-value.
d. What conclusion should we draw from the study?
Which test? Determine which chi-square test is appropriate in each of the following settings. Explain your reasoning.
a. With many babies being delivered by planned cesarean section, Mrs. McDonald’s statistics class hypothesized that there would be fewer younger people born on the weekend. To investigate, they selected a random sample of people born before and a separate random sample of people born after In addition to year of birth, they also recorded the day of the week on which each person was born.
b. Are younger people more likely to be vegan/vegetarian? To investigate, the Pew Research Center asked a random sample of U.S. adults for their age and whether or not they are vegan/vegetarian.
More candy The two-way table shows the results of the experiment
described in Exercise 27.
|Red Survey||Blue Survey||Control Survey||Total|
a. State the appropriate null and alternative hypotheses.
b. Show the calculation for the expected count in the Red/Red cell. Then provide a
complete table of expected counts.
c. Calculate the value of the chi-square test statistic.
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