Consider the following competing hypotheses and accompanying

Consider the following competing hypotheses and accompanying sample results. Use Table 2.

Calculate the value of the test statistic under the assumption that the difference is normally distributed.(Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

At the 5% significance level, what is the critical value? (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

Consider the following competing hypotheses and accompanying sample results. Use Table 2.

Hypotheses: H0: D 0; HA: D < 0

Sample results: = 4.4, sD = 6.0, n = 19

Solution

Formulating the null and alternative hypotheses,          
          
Ho:   uD   >=   0
Ha:    uD   <   0
          
          
Getting the test statistic, as          
          
X = sample mean =    -4.4      
uo = hypothesized mean =    0      
n = sample size =    19      
s = standard deviation =    6      
          
Thus, t = (X - uo) * sqrt(n) / s =    -3.196525892 [ANSWER, PART A]

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As we can see, this is a    1   tailed test.  
          
Thus, getting the critical t,          

df = n - 1 =    18      
tcrit =    -1.734063607   [ANSWER,B]

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Also, the p value is          
          
p =    0.002500266      
          
Comparing t and tcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.  

[OPTION A] Reject H0 since the value of the test statistic is less than the critical value.