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The mean annual premium for automobile insurance in the United States is $1,503. Being from Pennsylvania, you believe automobile insurance is cheaper there and wish to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1,440 with a standard deviation of s = $160.

• (a)Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.
  • H₀: < 1,503
  • H_a: 1,503
  • H₀: 1,503
  • H_a: > 1,503
  • H₀: 1,503
  • H_a: < 1,503
  • H₀: > 1,503
  • H_a: 1,503
  • H₀: = 1,503
  • H_a: 1,503

(b)What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.)$ _______________

(c)At = 0.05, test for a significant difference.

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

_________________

Find the p-value. (Round your answer to four decimal places.)

p-value = ______________

State your conclusion.

• Do not reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
• Reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
• Reject H₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
• Do not reject H₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.