Please provide solution with use of statistical software!!! We would like to est

Question

Please provide solution with use of statistical software!!!

We would like to estimate the true proportion p of all Canadian university students who have ever smoked marijuana. In a random sample of 200 students, 118 of them report to have tried the drug.  

(a)  Calculate a 90% confidence interval for the true proportion of all Canadian university students who have smoked marijuana.


(b) We would like to conduct a hypothesis test at the 10% level of significance to determine whether there is evidence that the majority of Canadian university students have tried marijuana. What are the hypotheses for the appropriate test of significance?

(c) What is the value of the test statistic for the appropriate test of significance?

(d) What is the P-value of the test?

(e) What is the correct conclusion for the test?

(f) Suppose we had instead conducted the test using the critical value method. What would be the decision rule and the conclusion?

(g) What is the rejection rule in terms of pˆ?


(h)  What is the power of the test if the true proportion of students who have actually tried marijuana is actually 0.6?

Explanation / Answer

A)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.59          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.034777867          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.0572045          
lower bound = p^ - z(alpha/2) * sp =   0.5327955          
upper bound = p^ + z(alpha/2) * sp =    0.6472045          
              
Thus, the confidence interval is              
              
(   0.5327955   ,   0.6472045   ) [ANSWER]

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b)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.5
Ha:   p   >   0.5 [ANSWER]

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c)

As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.59      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.035355339      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    2.545584412   [ANSWER]

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d)  
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.005454749   [ANSWER]

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e)
  
significance level =    0.1      

As P < 0.1, we   REJECT THE NULL HYPOTHESIS.      

Hence, there is significant evidence that the majority of Canadian university students have tried marijuana. [ANSWER]

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