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Chapter 9: Q.2.2 (page 539)
Describe a Type II error in this setting.
Type II error happens in the event that the null hypothesis isn't dismissed regardless of whether it isn't right.
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A confidence interval for a population mean is calculated to be . Assume that the conditions for performing inference are met. What conclusion can we draw for a test of role="math" localid="1650275427722" versus at the level based on the confidence interval?
(a) None. We cannot carry out the test without the original data.
(b) None. We cannot draw a conclusion at the level since this test is connected to the confidence interval.
(c) None. Confidence intervals and significance tests are unrelated procedures.
(d) We would reject at level .
(e) We would fail to reject at level .
Radon detectors Radon is a colorless, odorless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. Because radon is slightly radioactive, there is some concern that it may be a health hazard. Radon detectors are sold to homeowners worried about this risk, but the detectors may be inaccurate. University researchers placed a random sample of detectors in a chamber where they were exposed to picocuries per liter of radon over days. A graph of the radon readings from the detectors shows no strong skewness or outliers. The Minitab output below shows the results of a one-sample t interval. Is there significant evidence at the level that the mean reading differs from the true value ? Give appropriate evidence to support your answer.
Refer to Exercise 1. In Simon鈥檚 SRS, 16 of the students were left-handed. A significance test yields a P-value of 0.2184.
(a) Interpret this result in context.
(b) Do the data provide convincing evidence against the null hypothesis? Explain.
Is your food safe? Do you feel confident or not confident that the food available at most grocery stores is safe to eat? when a gallup poll asked this question, of the sample said they were confident." Callup announced the poll's margin of error for confidence as percentage points. Which of the following sources of error are included in this margin of error? Explain.
(a) Gallup dialed landline telephone numbers at random and so missed all people without landline phones, including people whose only phone is a cell phone.
(b) Some people whose numbers were chosen never answered the phone in several calls or answered but refused to participate in the poll.
(c) There is chance variation in the random selection of telephone numbers.
Paying high prices? A retailer entered into an exclusive agreement with a supplier who guaranteed to provide all products at competitive prices. The retailer eventually began to purchase supplies from other vendors who offered better prices. The original supplier filed a lawsuit claiming violation of the agreement. In defense, the retailer had an audit performed on a random sample of invoices. For each audited invoice, all purchases made from other suppliers were examined and compared with those offered by the original supplier. The percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded.For example, a data value of means that the price would be lower with a different supplier for of the items on the invoice. A histogram and some computer output
for these data are shown below. Explain why we should not carry out a one-sample t-test in this setting.
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