Safety of hybrid cars. According to the Highway Loss DataÂ Institute (HLDI), â€œHybrid [automobiles] have a safety edge over their conventional twins when it comes toÂ shielding their occupants from injuries in crashesâ€ (HLDI Bulletin, Sept. 2011). Consider data collected by the HLDI on Honda Accords. In a sample of 50,132 collision claims for conventional Accords, 5,364 involved injuries; in a sample of 1,505 collision claims for hybrid Accords, 137 involved injuries. You want to use this information to determine whether the injury rate for hybrid Accords is less than the injury rate for conventional Accords.
a. Identify the two qualitative variables measured for each Honda Accord collision claim.
b. Form a contingency table for this data, giving the number of claims in each combination of the qualitative variable categories.
c. Give H0 and Ha for testing whether injury rate for collision claims depends on Accord model (hybrid or conventional).
d. Find the expected number of claims in each cell of the contingency table, assuming that H0 is true.
e. Compute the x2 test statistic and compare your answer with the test statistic shown on the accompanying XLSTAT printout (below).
f. Find the rejection region for the test using a = .05 and compare your answer to the critical value shown on the accompanying XLSTAT printout.
g. Make the appropriate conclusion using both the rejection region method and the p-value (shown on the XLSTAT printout).
h. Find a 95% confidence interval for the difference between the injury rates of conventional and hybrid Honda Accords. (See Section 10.3.) Use the interval to determine whether the injury rate for hybrid Accords is less than the injury rate for conventional Accords.