A project conducted by the Australian Federal Office of Road Safety asked a random sample of people many questions about their cars. One question asked the reason for choosing their specific car. Do the data support the claim that the reasons for choosing a car are not equally likely? Test at the 10% level. Reason for Choosing a Car ReasonFrequencySafety49Reliability40Cost41Performance32Comfort32Looks50 State the hypotheses. H0: The reasons for choosing a car Select an answer are are not equally likely. Ha: The reasons for choosing a car Select an answer are not are equally likely. Calculate the χ2 test statistic. Round expected values to two decimal places when calculating the test statistic. Round χ2 to three decimal places. χ2 = Calculate the p-value. Round to four decimal places. p-value = State your decision. Since p-value ? ≤ > 0.10, Select an answer fail to reject reject H0. Interpret the results. At the 10% signficance level there Select an answer is is not enough evidence to conclude that the frequencies observed substantiate the claim that the reasons for choosing a car Select an answer are are not equally likely.
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- \( H_0 \): The reasons for choosing a car **are equally likely**. - \( H_a \): The reasons for choosing a car **are not equally likely**. --- Show more…
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A project conducted by the Australian Federal Office of Road Safety asked people many questions about their cars. One question was the reason that a person chooses a given car, and that data is in the given table ("Car preferences," 2013). Do the data show that the frequencies observed substantiate the claim that the reasons for choosing a car are equally likely? Test at the 5% level. Safety Reliability Cost Performance Comfort Looks 84 62 46 34 47 27 Use the framework below to guide your work. Hypotheses: : Ho: Frequencies observed substantiate the claim that the reasons for choosing a car are equally likely Ha: Frequencies observed substantiate the claim that the reasons for choosing a car are not equally likely Blank #1: With the assumption of Ho in that all are equally likely, the expected count of each cell is _______________. Blank #2: The degrees of freedom for the GOF test are _____________. Blank #3: Test statistic = _________ (round to one decimal place) Blank #2: p-value = __________ (round to four decimal places) Blank #3: Test decision: We decide to ___________ Ho (reject or do not reject) Blank #4: Conclusion back into the words of problem: The evidence __________(favors or does not favor) the claim that the reasons for choosing a car are not equally likely
Sri K.
Perform the indicated chi-square independence test by doing the following. (a) Identify the claim and state $H_{0}$ and $H_{a}$ (b) Determine the degrees of freedom, find the critical value, and identify the rejection region. (c) Find the chi-square test statistic. If convenient, use technology. (d) Decide whether to reject or fail to reject the null hypothesis. (e) Interpret the decision in the context of the original claim. You work for an insurance company and are studying the relationship between types of crashes and the vehicles involved in passenger vehicle occupant deaths. As part of your study, you randomly select 4270 vehicle crashes and organize the resulting data as shown in the contingency table. At $\alpha=0.05,$ can you conclude that the type of crash depends on the type of vehicle? (FIGURE CAN'T COPY)
Chi-Square Tests and the F-Distribution
Independence
Use the χ² test to test the claim that in the given contingency table, the row variable and the column variable are independent. Use the sample data below to test whether car color affects the likelihood of being in an accident. Use a significance level of 0.01. H₀: Car color and being in an accident are independent. H₀: Car color and being in an accident are dependent. Test statistics χ² = 0.4287 State your conclusion about H₀. A. Since the P-value = 0.4287 > 0.05, fail to reject H₀. B. Since χ² = 0.4287 > 0.05, fail to reject H₀. C. Since the P-value > 0.25, fail to reject H₀. D. Since the P-value < 0.25, reject H₀.
Adi S.
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