Question

A car manufacturer claims that 52% of Americans are interested in having internet access in their cars. In a simple random sample of 300 Americans, 161 stated they were interested in having web access in their cars. Test the hypothesis that more than 52% of Americans are interested in having internet access in their cars. Assume independence. Use .05 as the level of significance.

Complete the steps below:

a) Write the null and alternative hypotheses using proper notation.

b) Explain how each of the conditions of CLT are met.

c) Give the z-test statistic AND the p-value.

d) Using your p-value, what is your decision about the null hypothesis.

e) What is your conclusion regarding whether or not more than 52% of Americans are interested in having web access in their cars? Be sure to use the phrase statistically significant.  

Answer 1

Ho :   p =    0.52                  
H1 :   p >   0.52       (Right tail test)         
                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   161                  
Sample Size,   n =    300                  
                          
Sample Proportion ,    p̂ = x/n =    0.5367     

conditions:

np>5 and n(1-p)>5
npq>10
all satisfied
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0288                  
Z Test Statistic = ( p̂-p)/SE = (   0.5367   -   0.52   ) /   0.0288   =   0.5778
                                
                          
p-Value   =   0.2817 [Excel function =NORMSDIST(-z)             
Decision:   p value>α ,do not reject null hypothesis                       
conclusion: There is not statistically significant to say that  more than 52% of Americans are interested in having web access in their cars

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Please revert back in case of any doubt.

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