Question

1)

Give a 98% confidence interval, for μ1−μ2μ1-μ2 given the following information.

n1=35n1=35, ¯x1=2.26x¯1=2.26, s1=0.48s1=0.48
n2=40n2=40, ¯x2=2.11x¯2=2.11, s2=0.98s2=0.98

±±   Rounded to 2 decimal places.

2)

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. For the context of this problem, the first data set represents a pre-test and the second data set represents a post-test. You'll have to be careful about the direction in which you subtract.     

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 pre-test and post-test samples for n=42n=42 subjects. The average difference (post - pre) is ¯d=−3.8d¯=-3.8 with a standard deviation of the differences of sd=16.4sd=16.4.

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? Round to 4 decimal places.
   
   p-value =
   
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 mean difference of post-test from pre-test is less than 0.
   • There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.
   • The sample data support the claim that the mean difference of post-test from pre-test is less than 0.
   • There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.

Answer 1