For Exercises 51–58, do the following:

  1. State the hypotheses and the rejection rule.
  2. Calculate .
  3. Find the -value.
  4. State the conclusion and the interpretation.

Question 9.157

51. Car Insurance. Like sports cars? They can be expensive. Time.com/Money reports that in 2014 the mean annual car insurance premium for a Porsche Panamera Turbo-S was $3000. Suppose that a random sample of nine such Porsches taken this year has a mean car insurance premium of $3120. Assume , and assume that the distribution of premiums is normal. Test whether the population mean premium has increased, using level of significance .

9.3.51

(a) . We will reject if the . (b) (c) (d) The is not . Therefore we do not reject . There is insufficient evidence at level of significance that the population mean annual car insurance premium for a Porsche Panamera Turbo-S has increased from $3000.