Download P-Values in Hypothesis Testing: Problems and Solutions from Math 218, Fall 1999 and more Exams Mathematics in PDF only on Docsity! SAMPLE QUESTIONS INVOLVING P-VALUES TAKEN FROM MATH 218, FALL 1999 Problem 1. For which of the given P-values would the null hypothesis be rejected when performing a level 0.05 test? (a) .001 (b) 0.021 (c) 0.078 (d) 0.047 (e) 0.148 Problem 2. For a test of H0: µ ≤ 5 versus Ha : µ > 5, find the P-value associated with each of the following values of the test statistic. Assume that the population is normally distributed, and that the sample is large. (a) 1.4 (b) 0.9 (c) 1.9 (d) 2.4 (e) −0.1 Problem 3. Newly purchased automobile tires of a certain type are supposed to be filled to a pressure of 30 lb/in2. Let µ denote the true average pressure. Find the P-value associated with each of the following values of the test statistic for testing H0 : µ = 30 versus Ha : µ 6= 30. Assume that the population is normally distributed with a known variance. (a) 2.1 (b) −1.7 (c) = −0.5 (d) 1.4 (e) −5 Problem 4. A researcher collected data and calculated the sample mean and stan- dard deviation in order to test H0 : µ ≤ 17 versus Ha : µ > 17. Find a range of possible P-values for each of the given values of the test statistic with the given sample size. Assume normality. (a) 1.84;n = 15 (b) 3.74;n = 26 (c) 2.42;n = 14 (d) 1.32;n = 9 Problem 5. Find a range of possible P-values for a two-sided t-test for each case. (a) t = 2.3;n = 15 (b) t = −3.0;n = 26 (c) t = 4.2;n = 14 (d) t = −1.3;n = 9 Problem 6. Suppose a hypothesis test is performed of H0 : µ ≥ 10 versus Ha : µ < 10. The value of the test statistic is −2.1, using a sample size of 25. (The population standard deviation is not known.) If another sample this size were taken, what is the probability that the resulting test statistic would be smaller than −2.1? Problem 7. Suppose two people did the same hypothesis test on a population whose variance is known, one with a sample size of 25 and the other with a sample size of 50. Who do you think will get a smaller P-value? Problem 8. A manufacturer has developed a new fishing line, which he claims has a mean breaking strength of 15 kg or more. To test his claim a random sample of 25 lines is chosen. The sample has a mean breaking strength of 14.8 kg and a standard deviation of 0.5 kg. Find the P-value for this data and use it to decide whether the manufacturer’s claim can be rejected (at a level of significance 0.05). Assume normality.
