A news poll found that 73 of people are concerned about the

A news poll found that 73% of people are concerned about the possibility that their personal records could be stolen over the Internet. If a random sample of 200 college students at a certain university was taken and 158 were concerned about the possibility that their personal records could be stolen over the Internet, could a researcher conclude at the 0.025 level of significance that a higher proportion of the university\'s college students are concerned about Internet theft than the public at large?

Determine the null and alternative hypotheses

in this situation np= _____________ and n(1-p) =___________

what is the test statistic?

(THE CORRECT ANSWER IS 1.91 PLEASE EXPLAIN HOW THEY GOT THIS ANSWER)

what is the p-vaule

(THE CORRECT ANSWER IS 0.028 PLEASE EXPLAIN HOW THEY GOT THIS ANSWER)

What is the proper conclusion

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.73
Ha:   p   >   0.73 [ANSWER]

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Here,

np = 200*0.73 = 146
n(1-p) = 200*(1-0.73) = 54 [ANSWERS]

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As we see, the hypothesized po =   0.73      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.79      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.031392674      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.91127393   [answer, test statistic]

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As this is a    1   tailed test, then, getting the p value,  
          
p =    0.027984694      

[You can use technology or a z table to get the right tailed area for z = 1.91.]

significance level =    0.025      

Comparing p > 0.025, we   FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that a higher proportion of the university\'s college students are concerned about Internet theft. [CONCLUSION]