NAME:___________________________ MAT 1272 (Test 4) 1. In a hypothesis test with hypotheses and , a random sample of 112 elements selected from the population produced a mean of 52.8. Assume that and that the test is to be made at the 2% significance level. a) What is the critical value of the test statistic? b) Determine the value of the test statistic c) Should you reject or fail to reject the null hypothesis? 2. In a hypothesis test with hypotheses : = 90 and : 90, a random sample of 106 elements selected from the population produced a mean of 85.0. Assume that and that the test is to be made at the 5% significance level. a) What are the critical values of the test statistic? b) Determine the value of the test statistic. c) Should you reject or fail to reject the null hypothesis? 3. In a hypothesis test with hypotheses and a random sample of 24 elements selected from the population produced a mean of 60.0 and a standard deviation of 14.9. The test is to be made at the 10% significance level. Assume the population is normally distributed. a) What is the critical value of the test statistic? b) Determine the value of the test statistic. c) Should you reject or fail to reject the null hypothesis? 4. In a hypothesis test with hypotheses and a random sample of 16 elements selected from the population produced a mean of 91.5 and a standard deviation of 4.8. The test is to be made at the 5% significance level. Assume the population is normally distributed. a) What are the critical values of the test statistic? b) Determine the value of the test statistic. c) Should you reject or fail to reject the null hypothesis? 5. A company that manufactures light bulbs claims that its light bulbs last an average of 1,150 hours. A sample of 25 light bulbs manufactured by this company gave a mean life of 1096 hours and a standard deviation of 161 hours. A consumer group wants to test the hypothesis that the mean life of light bulbs produced by this company is less than 1,150 hours. The significance level is 5%. Assume the population is normally distributed. a) Set up the competing hypothesis 0: 1: b) What is the critical value of the test statistic. c) Determine the value of the test statistic d) Is there enough evidence to conclude that the mean life of light bulbs produced by this company is less than 1150 hours? 6. A researcher wants to test if the mean price of houses in an area is greater than $145,000. A random sample of 36 houses selected from the area produces a mean price of $149,000. Assume that and that the test is to be made at the 1% significance level. a) Set up the competing hypothesis 0: 1: b) What is the critical value of the test statistic. c) Determine the value of the test statistic. d) Is there enough evidence to show that the mean price of houses in that area is greater than $145,000