Problem 6 A statistics instructor believes that 50 of his st

(Problem 6) A statistics instructor believes that 50% of his students are male. One of his students thinks there are more males than females taking statistics, so he decides to conduct a random survey of past courses. He found that 83 of 150 students were male. Answer the questions below. HINT: This is a test of a single population proportion. See Example 9.17 on page 487 of the textbook.

(3 points each, 15 points total)

(a) What is the null hypothesis (Ho) and what is the alternate hypothesis (Ha)?
(b) What is the standard error of the proportion?
(c) What is the test statistic?
(d) What is the P-value for this test? HINT: Assume a normal distribution and use the single population proportion equations on page-502 of Illowsky.

(e) Is there sufficient evidence to reject the null hypothesis (Ho) at a 99% confidence level (=0.01)?

Solution

a)

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

**************************

b)

As we see, the hypothesized po =   0.5      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.040824829   [ANSWER, STANDARD ERROR]

*****************************

c)  

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.553333333      

Getting the z statistic,          
          
z = (p^ - po)/sp =    1.306394529   [ANSWER, TEST STATISTIC]

*************************

D)

As this is a    1   tailed test, then, getting the p value,  
          
p =    0.095709213   [ANSWER, P VALUE]  

******************************
As p < 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.      
There is no significant evidence that there are more male than female students. [CONCLUSION]