Question

A company of interest digitizes paper documents. The old software produced a mean of 5 errors per page. A random sample of 100 documents produced a sample mean of 4.730 errors per page. The standard deviation of errors per page is known to be 1. We want to know whether the new software changed the mean number of errors per page.

1. What is the null hypothesis and what is the alternative hypothesis?

2. What is the value of the test statistic?

3. What is the p-value of the test? (Compute to 4 digits).

4. Do we reject H0 at the .05 level of significance?

5. Do we reject H0 at the .01 level of significance?

Answer 1

1)

H0: = 5

Ha: 5

2)

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 4.730 - 5) / ( 1 / sqrt(100) )

= -2.7

3)

For two tailed test,

p-value = 2 * P(Z < z)

= 2 * P( Z < -2.7)

= 2 * 0.0035

= 0.0070

4)

Since p-value < 0.05 level , Reject H0

5)

Since p-value < 0.01 level, Reject H0