5Q - 11-1-1

A veterinarian keeps track of the types of animals treated by an animal clinic. The following distribution represents the percentages of animals the clinic has historically encountered.

If the animal clinic treats 230 animals in a month, how many of each animal type would be expected?

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A company claims they produce their mixed bag of candies so that, of the candies in the bag, 20 percent are dark chocolate, 60 percent are milk chocolate, and 20 percent are white chocolate. In a random sample of candies of size 50, the counts are as follows: 6 dark, 32 milk, and 12 white. Assuming the conditions for inference are met, what is the test statistic for a chi-square goodness-of-fit test to investigate whether the distribution of the sample is consistent with the company’s claim?

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Which of the following chi-square distributions has the smallest number of degrees of freedom?

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• Beef

• Chicken

• Fish

• Pork

• Vegetarian

A fisheries biologist collected a random sample of fish from a lake and conducted a chi-square goodness-of-fit test to see if the distribution of fish changed over time. The table below shows the distribution of fish that were put into the lake when it was originally stocked.

The biologist found evidence to reject the null hypothesis in favor of the alternative hypothesis. Which of the following represents the alternative hypothesis of the test?

• At least one of the fish proportions is different than the corresponding proportion when the lake was originally stocked.

• The proportions for the different fish types are the same as the corresponding proportions when the lake was originally stocked.

• The proportions are evenly distributed among fish types.

• At least one of the fish proportions is the same as the corresponding proportion when the lake was stocked.

• All of the fish proportions are different than the corresponding proportions when the lake was stocked.

Which of the following is not a condition for a chi-square goodness-of-fit test?

• Data should be collected using a random sample or randomized experiment.

• When sampling without replacement, the sample size cannot be greater than 10 percent of the population size.

• All expected counts should be greater than 5.

• The distribution of the sample should be approximately normal.

• During the sampling process, each individual chosen should be independent of the next.

For which of the following is a chi-square goodness-of-fit test most appropriate?

• Estimating a difference between two population means

• Estimating a difference between two population proportions

• Finding the expected value of a probability distribution

• Determining whether a categorical variable has a significantly different distribution of proportions than the expected distribution

• Determining the best shape for a set of data

A chi-square goodness-of-fit test where all assumptions were met yielded the test statistic χ²=12.4. Henry claims the corresponding p–value of 0.03 means that the probability of observing a test statistic of χ²=12.4 is 0.03, assuming the null hypothesis is true. Which of the following is a valid criticism of this interpretation of the p–value?

• The null hypothesis can never be assumed to be true.

• The null hypothesis is not stated.

• The p–value is not the probability of observing 12.4 exactly.

• The significance level is not stated.

• The degrees of freedom are not stated.

• The expected number of blue-collar workers donating to charity is less than 30.

• The expected number of management workers donating to charity is 100.

• The expected numbers of other white-collar and blue-collar workers donating to charity are the same.

• The expected number of other white-collar workers donating to charity is 50.

• The combined expected numbers of other white-collar and blue-collar workers donating to charity is greater than the expected number of management workers donating to charity.