Exam 9: Fundamentals of Hypothesis Testing: One-Sample Tests

If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000

A Type II error is committed when

If, as a result of a hypothesis test, you reject the null hypothesis when it is false, then you have committed

SCENARIO 9-4 A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower.If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one.A sample of size 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision. -Referring to Scenario 9-4, for a test with a level of significance of 0.10, the critical value would be .

Suppose we wish to test H0: $\mu$$\le$ 47 versus H1: $\mu$ > 47.What will result if we conclude that the mean is greater than 47 when its true value is really 52?

SCENARIO 9-8 One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase. The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance. -Referring to Scenario 9-8, the null hypothesis will be rejected if the test statistic is

SCENARIO 9-8 One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase. The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance. -Referring to Scenario 9-8, what critical value should the company officials use to determine the rejection region?

The symbol for the probability of committing a Type I error of a statistical test is

SCENARIO 9-1 Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to know if the mean number of defective bulbs per case is greater than 20 during the morning shift.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 cases: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$ Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ; One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject. -Referring to Scenario 9-1, the lowest level of significance at which the null hypothesis can be rejected is .

Which of the following would be an appropriate alternative hypothesis?

An entrepreneur is considering the purchase of a coin-operated laundry.The current owner claims that over the past 5 years, the mean daily revenue was $675 with a population standard deviation of $75.A sample of 30 days reveals a daily mean revenue of $625.If you were to test the null hypothesis that the daily mean revenue was $675 and decide not to reject the null hypothesis, what can you conclude?

If a researcher rejects a false null hypothesis, she has made a decision.

The smaller the p-value, the stronger is the evidence against the null hypothesis.

The symbol for the power of a statistical test is

SCENARIO 9-8 One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase. The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance. -Referring to Scenario 9-8, the value of the probability of committing aType II error $\beta$ is 0.95.

If the p-value is less than $\alpha$ in a two-tail test,

A pizza chain is considering opening a new store in an area that currently does not have any such stores.The chain will open if there is evidence that more than 5,000 of the20,000 households in the area have a favorable view of its brand.It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view.State the test of hypothesis that is of interest to the pizza chain. a) $H _ { 0 } : \pi \leq 0.32$ versus $H _ { 1 } : \pi > 0.32$ b) $H _ { 0 } : \pi \leq 0.25$ versus $H _ { 1 } : \pi > 0.25$ c) $H _ { 0 } : \pi \leq 5,000$ versus $H _ { 1 } : \pi > 5,000$ d) $H _ { 0 } : \mu \leq 5,000$ versus $H _ { 1 } : \mu > 5,000$

Suppose, in testing a hypothesis about a mean, the p-value is computed to be 0.043.The null hypothesis should be rejected if the chosen level of significance is0.05.

How many tissues should the Kimberly Clark Corporation package of Kleenex contain?Researchers determined that 60 tissues is the mean number of tissues used during a cold.Suppose a random sample of 100 Kleenex users yielded the following data on the numberof tissues used during a cold: $\bar { X } = 52$ , S = 22.Using the sample information provided, calculate the value of the test statistic.

SCENARIO 9-3 An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W. -Referring to Scenario 9-3, for this test to be valid, it is necessary that the power consumption for microwave ovens has a normal distribution.