Final answer:
A one-sample t-test will be used to determine if the sample mean of a two-year-old sedan significantly differs from the dealer's claim at a significance level of 0.05. Calculation of the t statistic will help decide whether to reject the dealer's claim.
Step-by-step explanation:
To determine whether there is enough evidence to reject the dealer's claim that the mean price of a two-year-old sedan is at least $20,500, we can perform a hypothesis test. Since we have a small sample size (14 vehicles), and we are assuming that the population is normally distributed, we should use the t-distribution for this test.
The null hypothesis (H0) is that the mean price is at least $20,500, and the alternative hypothesis (Ha) is that the mean price is less than $20,500. We will use a one-sample t-test to compare the sample mean to the dealer's claimed mean.
The test statistic is calculated using the formula:
t = (sample mean - claimed mean) / (standard deviation/sqrt(n)) = (19850 - 20500) / (1084/sqrt(14))
After calculating the test statistic, we compare it to the critical value from the t-distribution table at a significance level ( α ) of 0.05 with 13 degrees of freedom (n-1). If the test statistic is less than the critical value, we reject the null hypothesis and conclude that there is enough evidence to suggest that the mean price is less than the claim.