STA 2023,Fall 2011 Exam 4Sample

Question 1–5: In a random sample of 10,000 bulbs, 350 were found defective. At a significance level of 0.05, test the claim that the defective rate of such bulbs is less than 0.04.

  1. Identify H0, H1.
  1. Compute the test statistic. (2 decimal places)
  1. Compute the p-value. (4 decimal places)
  2. At a significance level of 0.05, does the sample provide sufficient evidence to support that that the defective rate of such bulbs is less than 0.04?
  1. If the actual defective rate of such bulbs is 0.03, what type of error does it introduce?

Question 6– 10: A recent study reveals that 280 out of 500 UF students prefer Coke, compared with Pepsi. At a significance level of 0.01, test a claim that half of UF students prefer Coke to Pepsi.

  1. Identify H0, H1.
  1. Compute the test statistic. (2 decimal places)
  1. Compute the p-value. (4 decimal places)
  2. At a significance level of 0.01, does the sample provide sufficient evidence to rejectthat half of UF students prefer Coke, not Pepsi?
  1. If the actual percentage is 0.5, what type of error does it introduce?

Questions11– 15: A random sample of 12 homes chosen from a town has a mean value of $92,460 and a standard deviation of $5200. At a significance level of 0.05, test a realtor’s claim that homes in this town have a mean value higher than $88,950.

  1. Identify H0, H1.
  1. Compute the test statistic. (2 decimal places)
  1. Find the range of the p-value.
  2. At a significance level of 0.05, does the sample provide sufficient evidence to support the realtor’s claim?
  1. If the actual mean price of homes in this town is $82,000, what type of error does it introduce?

Questions16–20: A random sample of 13 gas stations in Boca Raton has an average gasoline price of $3.89 per gallon and a standard deviation of $0.98 per gallon. At a significance level of 0.01, test the claim that the mean gasoline price in Boca Raton is different from $4.12 per gallon.

  1. Identify H0, H1.
  1. Compute the test statistic. (2 decimal places)
  1. Find the range of the p-value.
  2. At a significance level of 0.01, does the sample provide sufficient evidence that the mean gasoline price in Boca Raton is different from $4.12 per gallon?
  1. If the actual mean gasoline price in Boca Raton is $3.99 per gallon, what type of error does it introduce?