For Exercises 49–56, do the following:

  1. State the hypotheses.
  2. Find and the critical region.
  3. Find . Also, draw a standard normal curve showing , the critical region, and .
  4. State the conclusion and the interpretation.

Question 9.88

53. Gas Prices. The American Automobile Association reported in June 2011 that the mean price for a gallon of regular gasoline was $3.70. A recent random sample of 25 gas stations had a mean price of $3.90. Assume normality and . Test, using level of significance , whether the population mean price for a gallon of regular gasoline has risen since June 2011.

9.2.53

(a) (b) . Reject if . (c) .

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(d) Since is , the conclusion is reject . There is evidence at the 0.05 level of significance that the population mean price of regular gasoline is greater than $3.70 per gallon. Therefore we can conclude at the 0.05 level of significance that the population mean price for a gallon of regular gasoline has risen since June 2011.