Complete the following problem:
Q1. A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 950 hours. A random sample of 35 light bulbs has a mean life of 934 hours with a standard deviation of 80 hours. Do you have enough evidence to reject the manufacturer's claim? use a=0.04.
(a) Identify the null hypothesis and alternative hypotheses.
(b) Identify the critical value(s).
(c) Identify the standardized test statistic.
(d) Decide whether to reject or fail to reject the null hypothesis.
Q2. You believe that the mean annual kilowatt hour usage of U.S residential customers is less than 13,500. You find that a random sample of 34 residential customers has a mean kilowatt hour usage of 13,400 with a standard deviation of 304 kilowatt hours. You conduct a statistical experiment where Ho: mu >= 13,500 and Ha: mu < 13,500. At a = 0.01, decide whether to reject or fail to reject the null hypothesis.
Q3. A microwave oven repairer says that the mean repair cost for damaged microwave ovens is less than $100. You work for the repairer and want to test this claim. You find that a random sample of five microwave ovens has a mean repair cost of $104 and a standard deviation of $12.00. at alpha =0.05, do you have enough evidence to support the repairer's claim. Assume the population is normally distributed.
(a) Write the claim mathematically and identify H0 and Ha.
Which of the following correctly states H0 and Ha?
(b) Find the critical value(s) and identify the rejection region(s).
Which of the following graphs best depicts the rejection region for this problem?
(c) Find the standardized test statistic.
(d) Decide whether to reject or fail to reject the null hypothesis.
(e) Interpret the decision in the context of the original claim.
Q4. A medical researcher says that at least 22% of adults are smokers. In a random sample of 160 adults, 22.5% say they are smokers. At a = 0.01, do you have enough evidence to reject the researcher's claim?
(a) Which of the following correctly states H0 and Ha?
(b) Find the critical value(s) and identify the rejection region(s).
Which of the following graphs best depicts the rejection region for this problem?
(c) Find the standardized test statistic.
(d) Which of the following is the correct conclusion for the test?
Q5. Suppose it is known that if you offer free samples of a product, at least 57% of adults are more likely to buy the product. You interview a random sample of 50 adults. The results of the survey show that 38% of the adults said they were more likely to buy a product when there are free samples. A a = 0.01, can you reject the claim that at least 57% of the adults are more likely to buy a product when there are free samples?
Attachment:- Test statistics.rar