Consider the following hypotheses: H_0: mu 88. 8 H_A. mu > 88. 8 A sample of 40

Question

Consider the following hypotheses: H_0: mu 88. 8 H_A. mu > 88. 8 A sample of 40 observations yields a sample mean of 90. 3. Assume that the sample is drawn from a normal population with a known population standard deviation of 5. 0. Use Table 1. Calculate the p-value. (Round "z" value to 2 decimal places. ) What is the conclusion if a = 0. 02? Calculate the p-value if the above sample mean was based on a sample of 135 observations. (Round "z" value to 2 decimal places. ) What is the conclusion if a = 0. 02? The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 95. 5% of the people who have that disease. However, it erroneously gives a positive reaction in 5. 0% of the people who do not have the disease. Answer the following questions using the null hypothesis as "the individual does not have the disease. " What is the probability of Type I error? (Round your answer to 3 decimal places. ) What is the probability of Type II error? (Round your answer to 3 decimal places. )

Explanation / Answer

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   88.8  
Ha:    u   >   88.8  
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    90.3          
uo = hypothesized mean =    88.8          
n = sample size =    40          
s = standard deviation =    5          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.897366596 = 1.90          
              
Thus, the p value is              
              
p = 0.02871656 [ANSWER]  

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B)

As P > 0.02, we   DO NOT REJECT THE NULL HYPOTHESIS.   [ANSWER]      

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C)

Getting the test statistic, as              
              
X = sample mean =    90.3          
uo = hypothesized mean =    88.8          
n = sample size =    135          
s = standard deviation =    5          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.485685012 = 3.49          
              
Also, the p value is              
              
p = 0.00024151 [answer]

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D)
              
As P < 0.02, we   REJECT THE NULL HYPOTHESIS.   [ANSWER]     

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