1. If from a sample size of 64 a sample mean of 80 is found and the population standard deviation is known to be equal to 8. Construct a 95% confidence interval for the population mean.
2. Construct a 95% confidence interval for the mean based on the following data: 1,2,3,4,5,6,7.
3. A light bulb factory needs to test the hypothesis that the mean lifetime of bulbs is 370 hours. A sample of 25 lightbulbs is taken and the sample mean lifetime is found to be 365. The population standard deviation of lifetime of lightbulbs is known to be 10. (a) Perform the appropriate two-sided test to test the hypothesis at the 0.05 level of. (b)What is the p-value of the test.
4. In a random sample of 400 items 80 are found to be defective. The management wants to test the null hypothesis that the population defective rate is equal to 0.22. Test this hypothesis at the significance level of 0.01 (perform a two sided test).
5. Refer to 5. If your surname is A-K perform a lower tail test for the same problem, if your surname is L-Z perform an upper tail test, use the same significance level.