Question

1) You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. For the context of this problem, μd=PostTest−PreTestμd=PostTest-PreTest one data set represents a pre-test and the other data set represents a post-test. Each row represents the pre and post test scores for an individual.

      Ho:μd=0Ho:μd=0
      Ha:μd≠0Ha:μd≠0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

pre-test	post-test
55.7	49
48.8	45.7
49.4	56.9
42.3	46.4
55.2	69
39.2	39.3
45.9	49.5
40.7	47.4
54.7	72.1
32.6	44.7
56.6	70
53.2	41.6
35.8	53.2
59.3	74.1
34	50.6
45.7	60.5
55.2	70
50.4	53.8
50.8	47.7
58.8	65.3
44.3	25.6
54.1	55.8
58.8	73.1

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 4 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
• There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
• The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0.
• There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.

2)

Data about salaries showed that staff nurses in Tampa earn less than staff nurses in Dallas (The Tampa Tribune, Jan 15, 2007). You are a manager at a Tampa hospital and want to test the claim of the Tribune. You wish to test the claim at a significance level of α=0.01α=0.01. So you conduct a follow up survey of 40 staff nurses in Tampa and 29 staff nurses in Dallas. You find that the sample from Tampa showed an average salary of $56100 with a standard deviation of 5950, and the sample from Dallas showed an average salary of $58800 with a standard deviation of 7600.

(Assume both populations are normally distributed, but you do not know the standard deviations for either. Also, you have no reason to believe the variances of the two populations are equal.)

1. What is the test statistic for this sample?
   
   test statistic =  Round to 4 decimal places.
   
2. What is the p-value for this sample?
   
   p-value =  Round to 4 decimal places.
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
   • There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
   • The sample data support the claim that the first population mean is less than the second population mean.
   • There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.

Answer 1