1.Normal curve and the P-value.

A test statistic for a two-sided significance test for a population mean is z=2.47.Find the P-value. Report the P-value to 4 decimal places

2.Testing a random number generator.

Statistical software often has a "random number generator"that is supposed to produce numbers uniformly distributed between 0and 1.If this is true,the numbers generated come from a population with= 0.5. A command to generate 100 random numbers gives outcomes with mean= 0.469 and s = 0.286. Because the sample is reasonably large, take the population standard deviation also to be= 0.286. Do we have evidence that the mean of all numbers produced by this software is not 0.5?

(report to 2 decimal places) z =

(report to 2decimal places) p-value =

Is there evidence that the mean is not 0.5 (yes or no)?

3.State the appropriate null hypothesis H0 and alternative hypothesis Ha for the following case:

The student newspaper at your college recently changed the format of its opinion page. You want to test whether students find the change an improvement. You take a random sample of students and select those who regularly read the newspaper. They are asked to indicate their opinions on the changes using a five-point scale: -2 if the new format is much worse than the old, -1 if the new format is somewhat worse than the old, 0 if the new format is the same as the old, +1 if the new format is somewhat better than the old, +2 if the new format is much better than the old.

a.H0: u > 0

Ha: u = 0

b.H0: u = 2

Ha: u > 2

c.H0: u = 0

Ha: u does not equal 0

d.H0: u =2

Ha: u does not equal2

e.H0: u = 0

Ha: u> 0

f.H0: u > 2

Ha: u = 2