Statistics - Hypothesis Testing Projects

Manager claims average sales for her shop is $1800 a day during winter months. 10 winter days selected

Manager claims average sales for her shop is $1800 a day during winter months. 10 winter days selected at random, and the mean of the sales is $1830. The standard deviation of the population is $200. Can one reject the claim at a significance level of .05? Find the 95% confidence interval of the mean. Does the confidence interval interpretation agree with the hypothesis test results? Explain. Assume the variable is normally distributed.
Brand x and brand y of pain relievers were tested to see how much ibuprofen each table contained. Does brand x have more ibuprofen? Test at the .05 level.
A study of teenagers found the following information on length of time (in minutes) each talked on phone. Find the 95% confidence interval of the true differences in means.
Consumer advocate claims there is no difference in variance of number of hours that 2 companies' batteries will last. Sample of 10 batteries selected from company x, and the variance of hours is 24. Sample of 10 batteries from company y has a variance of 40. At a significance level of 0.10, test the claim that there is no difference in the variance of the life of the batteries.
Emergency team responds to calls in a mean time of 8.4 minutes with a standard deviation of .7. A new dispatching system is being tested to see if response time can be lowered. If a sample of 18 calls with the new system were answered in mean time of 7.8 minutes, test at the .05 level. State hypotheses and identify claim, find critical value(s), compute test value, make decision, summarize results.
Certain lottery claims that 10% of tickets win some prize. Sample of 50 tickets had 3 winners. At .01 level, test claim that proportion is 10%. State hypotheses and identify claim, find critical value(s), compute test value, make decision, summarize results.
Test at the .01 level claim that population variance is less than 158 if a sample of 10 had a variance of 164. State hypotheses and identify claim, find critical value(s), compute test value, make decision, summarize results.
Car gets mean of 18mpg. Test see if cheaper grade of gasoline made difference in gas miles at .01 level. Sample of 38 fill ups with cheaper gas got mean of 17.8mpg and standard deviation of 0.6. State hypotheses and identify claim, find critical value(s), compute test value, made decision, summarize results.