8.You may need to use the appropriateappendix tableortechnologyto answer this question.

According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for66randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively.

(a)Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (Enter != foras needed.)

H₀:

H_a:

(b)Repeat the preceding hypothesis test using the critical value approach.

State the null and alternative hypotheses. (Enter != foras needed.)

H₀:

H_a:

Find the value of the test statistic. (Round your answer to three decimal places.)