Consider the following hypothesis statement using 010 and d

Consider the following hypothesis statement using = 0.10 and data from two independent samples. Assume the population variances are equal and the populations are normally distributed. Complete parts a and b.

H0: 1 2 11

H1: 1 2 > 11

overbarX1 = 66.6 overbarx2 = 52.1

s1 = 16.5 s2 = 17.1

n1 = 19 n2 = 22

a) Calculate the appropriate test statistic and interpret the result.

The test statistic is ______ (round to 2 decimal places)

The critical value(s) is (are) ________ (round to 2 decimal places)

Because the test statistic falls / does not fall / is less than / is greater than , reject / do not reject the null hypothesis.

b) The p-value is _____ (round to 3 decimal places)

a)

A.

Since the p-value is

lessless

than the significance level,

rejectreject

the null hypothesis.

B.

Since the p-value is less / not less than the significance level, reject / do not reject the null hypothesis.

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   11  
Ha:   u1 - u2   >   11  
At level of significance =    0.1          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    66.6          
X2 =    52.1          
              
Calculating the standard deviations of each group,              
              
s1 =    16.5          
s2 =    17.1          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    19          
n2 = sample size of group 2 =    22          

Also, sD =    5.255502926          
              
Thus, the t statistic will be              
              
z = [X1 - X2 - uD]/sD =    0.665968614 = 0.67   [ANSWER, TEST STATISTIC]

******************************************      
              
where uD = hypothesized difference =    11          
              
Now, the critical value for Z is              
              
zcrit =    1.28 [ANSWER]

****************************************  
              
Because the test statistic is LESS THAN the critical value , DO NOT REJECT the null hypothesis.

********************************

b)

The P value for the right tailed area of z = 0.665968614 is

P = 0.252715581. [ANSWER]

********************************

B. Since the p-value is NOT LESS than the significance level, DO NOT reject the null hypothesis.