Do families and singles have the same distribution of cars? Use a level of significance of . Suppose that randomly selected families and randomly selected singles were asked what type of car they drove: sport, sedan, hatchback, truck, van/SUV. The results are shown in Table Do families and singles have the same distribution of cars? Test at a level of significance of .
The alpha value has been set at . Because , the null hypothesis, , will be rejected. As a result, the null hypothesis is rejected, whereas the alternative hypothesis is accepted. As a result, there is sufficient data to establish that the distribution of cars among families and singles is not equal.
Given in the question that, use a level of significance of . Suppose that randomly selected families and randomly selected singles were asked what type of car they drove: sport, sedan, hatchback, truck, van/SUV. The results are shown in Table 11.20. We need to test at a significance level that whether the families and singles have the same distribution of cars.
The null hypothesis is as follows:
: Car distribution is the same for families and singles.
The alternate hypothesis is as follows:
: Car ownership is not evenly distributed among families and singles.
The following formula can be used to calculate degrees of freedom:
number of columns
The table of observed values has already been provided. Let's now use the formula below to determine the predicted frequencies:
Let's use Excel to determine the expected (E) values, as shown below.
The independence test statistic is provided below;
is a test statistic.
Apply the formula to cell B17 and drag the same formula up to cell F18 to get . After that, add up the totals of the columns and rows. The following is a table of test statistics:
As a result, the test statistic is
In Excel, the p-value can be determined using the CHIDIST () formula, as illustrated below:
As a result, the value is zero.
use a solution sheet to solve the hypothesis test problem. Go to Appendix E for the chi-square solution sheet. Round expected frequency to two decimal places car manufacturers are interested in whether there is a relationship between the size of the car an individual drives and the number of people in the driver’s family (that is, whether car size and family size are independent).To test this, suppose that car owners were randomly surveyed with the results in Table . Conduct a test of independence.
|Family Size||Sub & Compact||Mid-size||Full-size||Van & Truck|
According to an avid aquarist, the average number of fish in a -gallon tank is , with a standard deviation of two. His friend, also an aquarist, does not believe that the standard deviation is two. She counts the number of fish in other -gallon tanks. Based on the results that follow, do you think that the standard deviation is different from two? Data:
The manager of "Frenchies" is concerned that patrons are not consistently receiving the same amount of French fries with each order. The chef claims that the standard deviation for a ten-ounce order of fries is at most oz., but the manager thinks that it may be higher. He randomly weighs orders of fries, which yields a mean of oz. and a standard deviation of two oz.
Determine the appropriate test to be used in the next three exercises.
An economist is deriving a model to predict outcomes on the stock market. He creates a list of expected points on the stock market index for the next two weeks. At the close of each day's trading, he records the actual points on the index. He wants to see how well his model matched what actually happened.
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