For 1 I do not know how to set up or work this problem For 2

For #1, I do not know how to set up or work this problem.

For #2, I am not sure what test at the 5% level means, does that mean our confidence is 95% and our alpha=.05?

1. A researcher claims that 90% of people trust DNA testing. In a survey of 100 people, 91 of them said that they trusted DNA testing. Test the researcher’s claim at the 1% level of significance.

2. A teacher’s union would like to establish that the average salary for high school teachers in a particular state is less than $52,500. A random sample of 20 public high school teachers in the particular state has a mean salary of $51,578 and a standard deviation of $4,415. Test the union’s claim at the 5% level.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.9
Ha:   p   =/=   0.9
As we see, the hypothesized po =   0.9      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.91      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.03      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    0.333333333      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.73888268      
significance level =    0.01      

As P > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant evidence that the proportion of those who trust DNA testing is not 90%. [ANSWER]  

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