AutoWrecks, Inc. sells auto insurance. AutoWrecks keeps close tabs on its customers' driving records, updating its rates according to the trends indicated by these records. AutoWrecks' records indicate that, in a "typical" year, roughly 70% of the company's customers do not commit a moving violation, 10% commit exactly one moving violation, 15% commit exactly two moving violations, and 5% commit three or more moving violations. This past year's driving records for a random sample of 100 AutoWrecks customers are summarized by the first row of numbers in the table below. That row gives this year's observed frequency for each moving violation category for the sample of 100 AutoWrecks customers. The second row of numbers gives the frequencies expected for a sample of 100 AutoWrecks customers if the moving violations distribution for this year is the same as the distribution for a "typical" year. The bottom row of numbers contains the following value for each of the moving violation categories. Answer the following to summarize the test of the hypothesis that there is no difference between this year's moving violation distribution and the distribution in a "typical" year. Use the 0.05 level of significance for the test. (a) Determine the type of test statistic to use. Type of test statistic: ▼(Choose one) (b) Find the value of the test statistic. (Round your answer to two or more decimal places.) (c) Find the p-value. (Round your answer to three or more decimal places.) (d)Can we reject the hypothesis that there is no difference between this year's moving violation distribution and the distribution in a "typical" year? Yes No −fOfE2 fE = −Observed frequencyExpected frequency2 Expected frequency
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
AutoWrecks, Inc. sells auto insurance. AutoWrecks keeps close tabs on its customers' driving records, updating its rates according to the trends indicated by these records. AutoWrecks' records indicate that, in a "typical" year, roughly 70% of the company's customers do not commit a moving violation, 10% commit exactly one moving violation, 15% commit exactly two moving violations, and 5% commit three or more moving violations.
This past year's driving records for a random sample of 100 AutoWrecks customers are summarized by the first row of numbers in the table below. That row gives this year's observed frequency for each moving violation category for the sample of 100 AutoWrecks customers. The second row of numbers gives the frequencies expected for a sample of 100
AutoWrecks customers if the moving violations distribution for this year is the same as the distribution for a "typical" year. The bottom row of numbers contains the following value for each of the moving violation categories.
Answer the following to summarize the test of the hypothesis that there is no difference between this year's moving violation distribution and the distribution in a "typical" year. Use the
level of significance for the test.
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