Question

please answer.

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

ANSWER::

1). Larry's car averages 32 miles/gallon. He switches to a new motor oil.He is driving for 3000 highway miles.Hence the null hypothesis he wants to test is therefore

Null Hypohesis : Larry's car gives a mileage of 32 miles/gallon after switching to new motor oil

Alternative hypothesis : Larry's car gives a milege of more than 32 miles/gllaon (because it is advertised that the new motor oil increses milege) In this case, let the milege be denoted as x. Since Larry wants to test the existing standard milege of 32 miles/gallon, we take . Let be the average milege after switching to the new motor oil. Then we have:

Versus

(Note: HE is interested in testing whether the new motor oil gives more milege. In order to doo this, if the null hypothesis is rejected, the alternative hypothesis will be accepted)

2). Here the language department is administering a listening test to students who passed the placement test.It is given that experience shows that the mean scores of a standard listening test is 24 ie . The listening test is administered to 40 students and let the score be denoted by x. The objective or the aim of the faculty is to check whether their(students who pass French test) performance is different.

Here the alternative hypothesis is that the test scores are not the same as the standard (24) oe not equal to 24.

3.) It is given that the mean time to pass through one maze by a mouse is 18 seconds. A student thinks that a loud noise will cause the mice to pass through the maze faster.  

Null Hypothesis: The average time to pass through the maze by a mice=18 sec.

Alternative hypothesis: The average time after a loud noise<18 sec.(since the student feels that after loud noise, the time reduces)

If as usual we let x to be the time taken for a mouse to pass through the maze after a loud noise then

versus

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