Question

Suppose a poll of adults asked, "Have you ever driven a car when you probably had too much alcohol to drive safely?" of the 300 men who answered, 186 (62%) said yes and 111 (37%) said no. The remaining three weren't sure. Of the 300 women, 84 (28%) said yes while 213 (71%) said no, and the remaining three weren't sure. (You may need to use a calculator. Round your answers to two decimal places.) (a) Ignoring those who said they weren't sure, there were 297 men asked, and 186 said yes, they had driven a car when they probably had too much alcohol. Does this provide statistically significant evidence that a majority of men in the population (that is, more than half) would say that they had driven a car when they probably had too much alcohol, if asked? Go through the four steps to test this hypothesis. (Use a 0.05 level of significance.) null hypothesis The proportion of men in the population who would say they had driven a car when they probably had too much alcohol is less than 0.5. alternative hypothesis The proportion of men in the population who would say they had driven a car when they probably had too much alcohol is less than test statistic = p-value = The null hypothesis can be rejected. We can conclude that a majority of men in the population would say they had driven a car when they probably had too much alcohol. . 0.5. (b). For the test in part (a), you were instructed to perform a one-sided test. Why do you think it would make sense to do so situation? If you do not think it made sense, explain why not.

Answer 1

Solution:

a)

Ho :   p =    0.5                  
H1 :   p >   0.5       (Right tail test)          
                          

Given that,

α =    0.05                  
x =   186
n =    297
                          
Sample Proportion ,    p̂ = x/n =    0.6262   
                          
Standard Error ,  SE = √( p(1-p)/n ) =   0.0290                  
Test Statistic, Z = ( p̂-p)/SE = (   0.6262 -   0.5   ) /   0.0290   = 4.3517
                             
p-Value   = 0.00001
Decision:   p-value < α , we reject null hypothesis  

Conclusion: The null hypothesis can be rejected. We can conclude that a majority of men in the population would say they had driven a car when they probably had too much alcohol

b)

Yes, it makes sense to use one sided test hypothesis, as we want to know the proportion is greater than half