a simple random sample of size n420 adults was asked their f

a simple random sample of size n=420 adults was asked their favorite ice cream flavor. of the 420 individuals surveyed, 158 responded that they preferred mocko-chocko flavor. do more than 30% of adults prefer mocko-chocko ice cream? Use alpha=.01 level of significance. a) what is the null hypothesis? b)what is the alternative hypothesis? c)what is the value of the test statistic? d) what is the p-value of your test statistic? e) what is your conclusion?

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.3 [ANSWER]

B)

Ha:   p   >   0.3 [ANSWER]

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c)

As we see, the hypothesized po =   0.3      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.376190476      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.02236068      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    3.40734168   [ANSWER]

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d)  
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.000327995   [ANSWER]

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e)  

As P < 0.01, we   REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that more than 30% of adults prefer mocko-chocko ice cream. [CONCLUSION]