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

Which of the following would be an appropriate alternative hypothesis?

In instances in which there is insufficient evidence to reject the null hypothesis,you must make it clear that this does not prove that the null hypothesis is true.

Instruction 9-1 Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.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 butterflies: $n = 46 ;$ Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82; Null Hypothesis: $H _ { 0 } : \mu \leq 20.000 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic = 2.09; One-Tailed Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject. -Referring to Instruction 9-1,the probability of committing a Type II error is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 18 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

For a given sample size n,if the level of significance (α)is decreased,the power of the test

A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

Suppose,in testing a hypothesis about a proportion,the p-value is computed to be 0.034.The null hypothesis should be rejected if the chosen level of significance is 0.01.

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

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

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

The marketing manager for a car manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300.The manager believes from previous information that the proportion is 0.30.Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags.If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30,which test would you use?

For a given level of significance (α),if the sample size n is increased,the probability of a Type II error (β)

Instruction 9-4 A drug company is considering marketing a new local anaesthetic.The effective time of the anaesthetic 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 anaesthetic is such that the effective time should be normal with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anaesthetic;otherwise,it will continue to produce the older drug.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 Instruction 9-4,what is the probability of making a Type II error if the mean effective time of the anaesthetic is 7.5 using a 0.05 level of significance?

Instruction 9-4 A drug company is considering marketing a new local anaesthetic.The effective time of the anaesthetic 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 anaesthetic is such that the effective time should be normal with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anaesthetic;otherwise,it will continue to produce the older drug.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 Instruction 9-4,what is the power of the test if the mean effective time of the anaesthetic is 7.0 using a 0.05 level of significance?

Instruction 9-1 Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.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 butterflies: $n = 46 ;$ Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82; Null Hypothesis: $H _ { 0 } : \mu \leq 20.000 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic = 2.09; One-Tailed Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject. -Referring to Instruction 9-1,the power of the test is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 18 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

Instruction 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 Instruction 9-3,for this test to be valid,it is necessary that the power consumption for microwave ovens has a normal distribution.

"Is the intended sample size large enough to achieve the desired power of the test for the level of significance chosen?" should be among the questions asked when performing a hypothesis test.

Instruction 9-6 The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture.She performs a two-tailed test of the null hypothesis that the mean for the stressed oak furniture is 650.The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test. -Referring to Instruction 9-6,suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650.What would be the p-value of this one-tailed test?

Instruction 9-4 A drug company is considering marketing a new local anaesthetic.The effective time of the anaesthetic 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 anaesthetic is such that the effective time should be normal with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anaesthetic;otherwise,it will continue to produce the older drug.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 Instruction 9-4,what is the probability of making a Type II error if the mean effective time of the anaesthetic is 7.0 using a 0.10 level of significance?

Instruction 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 Instruction 9-3,what is the probability of making a Type II error if the mean power consumption of all such microwave ovens is in fact 257.3 W using a 0.05 level of significance?

Instruction 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 Instruction 9-3,the null hypothesis will be rejected at 1% level of significance.