A simple randorn sample of size $n=200$ drivers with a valid driver's license is asked if they drive an American-made automobile. Of the 200 drivers surveyed, 120 responded that they drive an American-made automobile. Determine if a majority of those with a valid driver's license drive an American-made automobile at the $\alpha=0.05$ level of significance. What type of variable is "drive an American-made automobile, or not"? A. Qualitative with more than two possible outcomes B. Discrete C. Qualtative with two possible outcomes D. Continuous What type of hypothesis test is appropriate to conduct for this research? A. Hypothesis test on a population standard deviation B. Hypothesis test on a population mean c. Hypothesis test on a population proportion Determine the nul and alkernative hypotheses. \[ \begin{array}{l|l|l|} H_{0}: & T \\ H_{1}: & T & T \\ \hline \end{array} \] (Type integers or decimals. Do not round.)
Solution
Step 1 ：The type of variable 'drive an American-made automobile, or not' is a qualitative variable with two possible outcomes. This is because the variable can only take on two possible outcomes: yes or no.
Step 2 ：The type of hypothesis test appropriate to conduct for this research is a hypothesis test on a population proportion. This is because we are dealing with a binary variable and we are interested in the proportion of drivers who drive an American-made automobile.
Step 3 ：The null and alternative hypotheses are: \n\n\[\begin{array}{l|l|l|}H_{0}: & p \leq 0.5 \H_{1}: & p > 0.5 \\hline\end{array}\]\n\nwhere \(p\) is the proportion of drivers who drive an American-made automobile. The null hypothesis is that a majority (more than 50%) of those with a valid driver's license do not drive an American-made automobile. The alternative hypothesis is that a majority of those with a valid driver's license do drive an American-made automobile.
