Dentists believe that 53% of the general population suffers from tooth decay. Th

Question

Dentists believe that 53% of the general population suffers from tooth decay. The makers of Toothy Grin Toothpaste believe that using their product reduces tooth decay, and in order to support their claim study a random sample of 2000 Toothy Grin users. It turns out that 1010 of these are suffering from tooth decay. The evidence is investigated to see whether these figures present enough evidence to indicate a decrease in tooth decay for the Toothy Grin users (Use a 0.05 significance level). what is the hypothesis? what is the z-stat? what is the p value?reject or retain

Explanation / Answer

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.53
Ha:   p   <   0.53 [HYPOTHESES]

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As we see, the hypothesized po =   0.53      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.505      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.011160197      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.2401038   [ANSWER, Z STAT]

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As this is a    1   tailed test, then, getting the p value, by table/technology,  
          
p =    0.012542092   [ANSWER]

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As P < 0.05, we   REJECT THE NULL HYPOTHESIS.      

There is significant evidence to indicate a decrease in tooth decay for the Toothy Grin users. [CONCLUSION]

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