a Write the claim mathematically and idenentify H0 and Ha b

(a) Write the claim mathematically and idenentify H0 and Ha. (b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the null hypothesis.

An environmental agency recently claimed that more than 32% of consumers have stopped buying a certain product because of the environmental concerns. In a random sample of 1080 consumers, you find 40% have stopped buying the product. At alpha=0.01, do you have enough evidence to support the claim?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.32
Ha:   p   >   0.32 [PART A]

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The critical value for a right tailed z test at 0.01 significance is, by table or technology,

zcrit = 2.326347874 [PART B]

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As we see, the hypothesized po =   0.32      
As it is given,          
          
po =    0.32      
          
Getting the standard error of po, spo,          
          
spo = sqrt[po (1 - po) / n] =    0.014194417      
          
Getting the z statistic,          
p^ =    0.4      

z = (p^ - po)/spo =    5.63601862 [PART C]
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As this is a    1   tailed test, then, getting the p value,  
          
p =    1.74027E-08      
significance level =    0.01      

Comparing p and the significance value, we   REJECT THE NULL HYPOTHESIS. [PART D]

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