In a study, people were observed for about 10 seconds in public places, such as malls and restaurants, to determine whether they smiled during the randomly chosen 10second interval. The researchers found that 325 males smiled, and 379 males did not smile. They also found that 445 females smiled, and 426 females did not smile. (Treat this data as if it were two simple random samples.)
a) Fill in the following table.

Males 
Females 
Number who smiled () 
325 
445 
Total number in sample ( 
704 
871 
Proportion who smiled () 
0.462 
0.511 
b) Find the pooled sample proportion estimate .
c) Suppose we want to test the claim that males are less likely to smile than females. State the null and alternative hypotheses for such a test. (Use )
d) Calculate the test statistic and specify the critical value
e) Find the Pvalue.
f) State the initial conclusion regarding the null hypothesis .
g) State the final conclusion in your own words that addresses the original claim.
h) Would your conclusion change if was used? Why or why not
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