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

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 0.10 level of significance?

Instruction 9-2 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: $H _ { 0 } : \mu \leq 20.000 ; a = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ; One-Tailed Test Upper CriticalValue $= 1.3006 ; p$ value $= 0.021$ ; Decision $=$ Reject. -Referring to Instruction 9-2,the power of the test is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 30 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

Instruction 9-1 A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses. Suppose in actuality that if someone is studying a business major, she can correctly identify that person as a business student 87% of the time. When a person is studying a science major, the student will incorrectly identify that person as a business student 16% of the time. Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major), she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student. -Referring to Instruction 9-1,what is the "actual confidence coefficient"?

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 power of the test if the mean power consumption of all such microwave ovens is in fact 248 W using a 0.10 level of significance?

Instruction 9-5 A bank tests the null hypothesis that the mean age of the bank's mortgage holders is less than or equal to 45 years, versus an alternative that the mean age is greater than 45 years. They take a sample and calculate a p-value of 0.0202. -Referring to Instruction 9-5,the null hypothesis would be rejected at a significance level of α = 0.01.

In testing a hypothesis,statements for the null and alternative hypotheses as well as the selection of the level of significance should precede the collection and examination of the data.

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.

Instruction 9-7 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: $H _ { 0 } : \mu \leq 20.000 ; a = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ; One-Tailed Test Upper CriticalValue $= 1.3006 ; p$ value $= 0.021$ ; Decision $=$ Reject. -Referring to Instruction 9-7,the biologist can conclude that there is sufficient evidence to show that the mean number of parasites per butterfly is greater than 20 with no more than a 1% probability of incorrectly rejecting the true null hypothesis.

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 greater than 650.Then if the test is performed with a level of significance of 0.10,the null hypothesis would be rejected.

A manager of the credit department for an oil company would like to determine whether the mean monthly balance of credit card holders is equal to $75.An auditor selects a random sample of 100 accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65.If you wanted to test whether the mean balance is different from $75 and decided to reject the null hypothesis,what conclusion could you reach?

Instruction 9-2 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: $H _ { 0 } : \mu \leq 20.000 ; a = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ; One-Tailed Test Upper CriticalValue $= 1.3006 ; p$ value $= 0.021$ ; Decision $=$ Reject. -Referring to Instruction 9-2,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 30 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

For a given level of significance,if the sample size is increased,the probability of committing a Type I error will increase.

The power of a test is measured by its capability of

Data snooping is occasionally permissible but is dependent on the construction quality of the study.

Which of the following would be an appropriate null hypothesis?

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,if the test is performed with a level of significance of 0.10,the engineer can conclude that the mean amount of force necessary to produce cracks in stressed oak furniture is 650.

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 0.10 level of significance?

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

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,for a test with a level of significance of 0.10,the critical value would be ________.

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