You are testing the null hypothesis that = 0 versus the alternative > 0 using =

Question

You are testing the null hypothesis that = 0 versus the alternative > 0 using = .05. Assume = 19. Suppose x = 4.6 and n = 16. Calculate the test statistic and its P-value. Repeat assuming the same value of x but with n = 26. Do the same for sample sizes of 36, 46, and 56. (Round the test statistic to two decimal places. Round the P-value to four decimal places.)

Plot the values of the test statistics versus the sample size. Do the same for the P-values. (Do this on paper. Your instructor may ask you to turn this in.) Summarize what this demonstration shows about the effect of the sample size on significance testing.

a. As sample size increases, a test becomes more significant.

b. As sample size increases, a test becomes less significant.    

c. As sample size increases, there is no effect on the significance.

d. As sample size decreases, a test becomes more significant.

n = 16: z P-value n = 26: z P-value n = 36: z P-value n = 46: z P-value n = 56: z P-value

Explanation / Answer

(a) A university gives credit in first-year calculus to students who pass a placement test. The mathematics department wants to know if students who get credit in this way differ in their success with second-year calculus. Scores in second-year calculus are scaled so the average each year is equivalent to a 74. This year 22 students who took second-year calculus passed the placement test.

Answer: b. H0: = 74; Ha: 74

(b) Experiments on learning in animals sometimes measure how long it takes a mouse to find its way through a maze. The mean time is 22 seconds for one particular maze. A researcher thinks that playing rap music will cause the mice to complete the maze slower. She measures how long each of 16 mice takes with the rap music as a stimulus.

Answer: a. H0: = 22 sec; Ha: < 22 sec

c) The average square footage of one-bedroom apartments in a new student-housing development is advertised to be 850 square feet. A student group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion.

Answer: e. H0: = 850 ft2; Ha: < 850 ft2

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