Hello, I have some questions about STAT that I want to someone can help me. Plea

Question

Hello, I have some questions about STAT that I want to someone can help me. Please give me detailed solutions. Thank you!!

During the 1980s, the general consensus is that about 5% of the nation's children had autism. Some claimed that increases certain chemicals in the environment has led to an increase in autism. (a) Write an appropriate hypothesis for this situation (b) A recent study examined 384 children and found that 46 showed signs of autism. Perform a test of the hypothesis and state the p-value. (c) What are your conclusions? State how you use the p-value.

Explanation / Answer

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.6
Ha:   p   =/=   0.6
As we see, the hypothesized po =   0.6      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.5      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.040824829      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.449489743      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.014305878      
significance level =    0.05      

As P < 0.05, we REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that the proportion of all homeowners that move to another house within 5 years from the time they purchased their first house is not 60%. [CONCLUSION]  

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