8.1

1) A climate researcher knows that it has previously been the case that the mean temperature in her city has been73.5 F. She suspects that this may no longer be the case and that the mean temperature may now have changed, and she suspects that is has risen in recent times. She collects sample data with the aim of conducting a hypothesis test to examine her suspicions.

Select the correct null and alternative hypotheses for this test:

A) H₀: = 73.5 F

H_A: 73.5 F

B) H₀: = 73.5 F

H_A: = 73.5 F

C) H₀: = 73.5 F

H_A: 73.5 F

D) H₀: = 73.5 F

H_A: > 73.5 F

E) H₀: = 73.5 F

H_A: 73.5 F

F) H₀: = 73.5 F

H_A: < 73.5 F

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2)

A group of home-brewers have always used a particular method of brewing beer. With the same amount of ingredients each time, their brews contain an average of = 13.737gallons of beer. The standard deviation is = 1.321gallons.

Rudy has a new and cheaper brewing method. While it is cheaper, Rudy suspects that it will decrease their productivity. The group decide to collect a sample of brewing amounts and conduct a hypothesis test on the mean amount of brew created by the new method. They will be using the value = 1.321as their population standard deviation. The null and alternative hypotheses are set to be:

H₀: = 13.737

H_A: < 13.737

Before they collect a sample or do the test, Sam thinks about the new brewing method. He suspects that, while it may decrease the average amount of brew created, it may actually increase it instead. Sam suggests that the alternative hypothesis should simply state that the population mean is not equal to 13.737:

H₀: = 13.737

H_A: 13.737

Sam believes that:

A) instead of conducting a two-tail test, they should conduct a one-tail test.

B) instead of conducting a one-tail test, they should conduct a two-tail test.

C) instead of conducting the particular two-tail test that was proposed, they should conduct a different kind of two-tail test.

D) instead of conducting the particular one-tail test that was proposed, they should conduct a different kind of one-tail test.

Answer: _____

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8.3

1) A hypothesis test is to be performed in order to test the proportion of people in a population that have some characteristic of interest. Select all of the pieces of information that are needed in order to calculate the test statistic for the hypothesis test:

A) the level of significance used

B) the characteristic of interest

C) the actual population proportion

D) the proposed population proportion

E) the size of the sample selected

F) the sample proportion calculated

Answers: _____

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2) You may find thestandard normal tableuseful in answering this question. Consider the hypothesis test with the following null and alternative hypotheses:

H₀:= 0.5

H_A:> 0.5

If the level of significance used is = 0.1, the region of rejection is the set of numbers:

A) whose absolute value is greater than 1.28

B) whose absolute value is less than 1.28

C) less than -1.28

D) whose absolute value is less than 1.645

E) greater than 1.645

F ) less than -1.645

G) greater than 1.28

H) whose absolute value is greater than 1.645

Answer_____

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3) Painadol is a well trusted, popular pain-killer used by millions throughout the country. Recently an epidemic of headaches has hit the nation and the manufacturers of Painadol have created a new, stronger painkiller called Painadene. The manufacturers are interested in testing whether the speed of pain relief is different with Painadene. It is known that the mean time taken by Painadol tablets to relieve pain is 34 minutes and the standard deviation is 5 minutes.

The manufacturers would like to construct a hypothesis test for the mean time () taken for Painadene tablets to relieve pain assuming the same population standard deviation () as the Painadol tablets. A random sample of 39 people with headaches tried the new Painadene tablets and the mean time taken to relieve the pain was calculated as 32.61 minutes. The hypotheses that will be used by the manufacturers areH₀: = 34andH_A: 34.

You may find thisstandard normal tableuseful throughout the following questions.

a)Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer as a decimal to 3 decimal places.

z =________

b)Using the test statistic for Painadol's hypothesis test and a level of significance of = 0.1, Painadol shouldaccept

reject or not rejectthe null hypothesis.

Answer: ______