An insurance agent says that the mean cost of insuring a two-year-old sedan (in good condition) is less than $1200. A random sample of 7 similar insurance quotes has a mean cost of $1125 and a standard deviation of $55. Is there enough evidence to support the agent’s claim at α = 0.10? Assume the population is normally distributed.
a. Identify the claim and state H0 and Ha.
b. Identify the level of significance α and the degrees of freedom.
c. Find the critical value t0 and identify the rejection region.
d. Find the standardized test statistic t. Sketch a graph.
e. Decide whether to reject the null hypothesis.
f. Interpret the decision in the context of the original claim.