problem1) Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. What would be the teststatistic to test DullCo's hypothesis?

problem2) What are the null and alternative hypotheses for the Dullco test?

problem3) In the Dullco ex, we would be performing what type of hypothesis test?

problem4) If α=.02, what would be the critical value for the Dullco test?

problem5) What is the risk of type I error if the U.S. military mobilizes troops to prepare for a missile attack from North Korea, but North Korea does not carry out an attack? Who will likely bear the costs of this error?

problem6) If a manager is told that there is possibly a safety issue related to a manufacturing process under their purview but decides not to run tests to detect the problem, what type of error is the manager exposed to?  What are the consequences of this type of error, and to whom?

problem7) If a research and development team is testing a new blood pressure medicine to see if it maintains patients’ average blood pressure at a significantly lower level than does the current industry standard, what sets of hypotheses would they use?

problem8) When do we make use of chi-squared tests and/or F-tests? In other words, what parameter do we want to know about, and which statistics are we using to make inferences about this parameter?

problem9) Which of the following statements is (are) true when we reject the null hypothesis?

a) The find outd value associated with our sample is extreme enough that we find it unlikely that this level of difference is merely due to chance.
b) We conclude that there is not enough difference in the sample for us to consider taking action.
c) The probability of a value as extreme or more extreme that the value we observed is smaller than the probability we chose as our “cutoff” point (the value at which we begin to conclude that there is a statistically significant difference).
d) Both a. and c. are correct.

problem10) Which of the following is true of paired T-tests?

a) One time they are used is when two samples are taken on the same individuals.
b) They are never used for “before and after” tests.
c) They are only used when σ2 is known
d) The paired t-test is preferred to chi-squared tests because it is more conservative.

problem11) If two CNC machine shops were competing for a contract to make rivets to a certain specification, what test would we use to test if there were differences in the variability of their products?

problem12) True or False? The degrees of freedom for the t-test used to compare two population means (independent samples) with unknown variances (assumed equal) will be n1 + n2 - 2.

problem13) True or False? The test statistic (F-find outd value) in an F test for equal variances is the ratio of the sample variances.

problem14) In a left-tailed test comparing two means with variances unknown but assumed to be equal, the sample sizes were n1 = 8 and n2 = 12. At α = .05, the critical value would be:

problem15) True or False? Alpha and beta can never be simultaneously reduced, even though that would be a desirable situation. describe your answer.