Question

1. Each of the following situations requires a significance test about a population mean μ. State the appropriate null hypothesis, H0, and alternative hypothesis, Ha, in each case. [Use words and/or symbols to state these]

• Larry’s car averages 32 miles per gallon on the highway. He switches to a new motor oil that is advertised as increasing gas mileage. After driving 3000 highway miles with the new oil, he wants to determine if his gas mileage actually has increased.
• A university gives credit in a French language course to students who pass a placement test. The language department wants to know if students who get credit in this way differ in their understanding of spoken French from students who actually take the French course. Some faculty think the students who test out of the course are better, but others argue that they are weaker in oral comprehension. Experience has shown that the mean score of students in the course on a standard listening test is 24. The language department gives the same listening test to a sample of 40 students who passed the placement test to see if their performance is different.
• Experiments on learning in animals sometimes measure how long it takes a mouse to find its way through a maze. The mean time is 18 seconds for one particular maze. A student thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a noise as stimulus.

Answer 1

Situation 1:

Null hypothesis: The average gas miles using the new motor oil is same as 32 .

Alternate hypothesis: The average gas miles using the new motor oil is greater than 32

Situtation 2:

Null hypothesis: The oral comprehension performance (average listening test score) of the placement students is same as 24 .

Alternate hypothesis: The oral comprehension performance (average listening test score) of the placement students is other than 24 .

Situtation 3:

Null hypothesis: The average time taken by mice to complete one particular maze under noise stimulus is same as 18 seconds.

Null hypothesis: The average time taken by mice to complete the particular maze under noise stimulus is significantly lesser than 18 seconds.