Among 2450 randomly selected male car occupants over the age of 8, 76% wear seatbelts. Among 2900 randomly selected female car occupants over the age of 8, 74% wear seat belts. Use a 0.1 significance level to test the claim that both genders have the same rate of seat belt use. Does there appear to be a gender gap? a. There appears to be a gender gap because there is not a significant difference in the proportions.
b. There does not appear to be a gender gap because there is a significant difference in the proportions.
c. There does not appear to be a gender gap because there is not a significant difference in the proportions.
d. There appears to be a gender gap because there is a significant difference in the proportions.

The correct option is D

Step-by-step explanation:

From the question we are told that

   The sample size for male car occupant is  

   The number that wear seat belt is

   The sample size for female car occupant is

   The number that wear a seat belt is  

Generally the population proportion is mathematically represented as

=>    

=>  

The sample proportion for male  car occupant is  

=>    

=>    

The sample proportion for female car occupant is  

=>    

=>    

The null hypothesis is  

The alternative hypothesis is  

Generally the standard error is mathematically represented as

=>      

=>    

Generally the test statistics is mathematically represented as

=>  

=>  

From the z table  the area under the normal curve to the right  corresponding to  3.37 is  

Generally the p-value is mathematically represented as

From the value obtained we see that    hence  

The decision rule is  

  Reject the null hypothesis

The conclusion is

 There appears to be a gender gap because there is a significant difference in the proportions

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.