Question

Are blonde female college students just as likely to have boyfriends as brunette female college students? 402 of the 657 blondes surveyed had boyfriends and 493 of the 766 brunettes surveyed had boyfriends. What can be concluded at the αα= 0.01 level of significance?

For this study, we should use Select an answer z-test for a population proportion t-test for the difference between two independent population means t-test for the difference between two dependent population means z-test for the difference between two population proportions t-test for a population mean

1. The null and alternative hypotheses would be:   
2.   

H0:H0:  Select an answer p1 μ1  ? ≠ > < =  Select an answer μ2 p2  (please enter a decimal)   

H1:H1:  Select an answer μ1 p1  ? = > ≠ <  Select an answer p2 μ2  (Please enter a decimal)

2. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
3. The p-value =  (Please show your answer to 4 decimal places.)
4. The p-value is ? ≤ >  αα
5. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.

Answer 1

To Test :-

H0 :- P1 = P2

H1 :- P1 P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 402 + 493 ) / ( 657 + 766 )
= 0.629

Z = -1.23

Test Criteria :-
Reject null hypothesis if

= -1.23 > -2.58, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( Z < -1.23 )
P value = 0.2186
Reject null hypothesis if P value <
Since P value = 0.2186 > 0.01, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is sufficient evidence to support the claim that  blonde female college students just as likely to have boyfriends as brunette female college students.