Problem
During a busy work week, your aging vehicle finally breaks down and the mechanic declares that fixing the car would cost more than it is worth. You then go to a dealer later that day and make a hasty decision to begin renting a used vehicle, agreeing to a payment plan of $\$ 195$ monthly so that your work is not interrupted. Over the weekend, you decide to investigate whether the average for similar vehicles is either above or below your payment plan. You gather a randomly selected sample of 30 similar vehicles from a dealer in your area and find an average monthly payment of 210 with a standard deviation of 17 . To check the conditions for this hypothesis test mark all of the following that apply. This is a random sample or a randomized experiment. This is not a random sample nor a randomized experiment. These observations are independent because $n \leq 0.05 N$, since the population of all similar cars is likely more than 600 . These observations are not independent because $n>0.05 N$, since the population of all similar cars is likely more than 600 The population is normally distributed. The population has a distribution with an unknown shape. The sample size is greater than or equal to $30, n \geq 30$ The sample size is less than $30, n<30$ Are the conditions met to compute the Hypothesis test? yes no
Solution
Step 1 ：This is a random sample or a randomized experiment.
Step 2 ：These observations are independent because \( n \leq 0.05 N \), since the population of all similar cars is likely more than 600.
Step 3 ：The sample size is greater than or equal to \( 30, n \geq 30 \)
Step 4 ：The population has a distribution with an unknown shape.
Step 5 ：Final Answer: \(\boxed{\text{yes}}\)
