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A climate researcher knows that it has previously been the case that the mean temperature in his city has

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A climate researcher knows that it has previously been the case that the mean temperature in his city has

been 74.5 °F. He suspects that this may no longer be the case and that the mean temperature may now have changed, and he suspects that is has risen in recent times. He collects sample data with the aim of conducting a hypothesis test to examine his suspicions.

Select the correct null and alternative hypotheses for this test:

H0: μ = 74.5 °FHA: μ > 74.5 °F H0: μ = 74.5 °FHA: μ ≤ 74.5 °F
 
H0: μ = 74.5 °FHA: μ ≥ 74.5 °F H0: μ = 74.5 °FHA: μ ≠ 74.5 °F
 
H0: μ = 74.5 °FHA: μ = 74.5 °F H0: μ = 74.5 °FHA: μ < 74.5 °F

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 ofμ = 13.737 gallons of beer. The standard deviation is σ = 1.321 gallons.

Rudy has a new brewing method and suspects that it will increase 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 σ = 1.321 as their population standard deviation. The null and alternative hypotheses are set to be:

H0: μ = 13.737

HA: μ > 13.737

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

H0: μ = 13.737

HA: μ ≠ 13.737

Sam believes that:

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