Question

USE THE FOLLOWING DIRECTION FOR 1A AND 1B: In 2010, a random sample of 250 dog owners was taken and it was found that 140 owned more than one dog. Recently, a random sample of 400 dog owners showed that 200 owned more than one dog. Do these data indicate that the proportion of dog owners owning more than one dog has decreased? Use a 5% level of significance, and p1= proportion of dog owners who owned more than one dog in 2010. If you conduct hypothesis testing, you have to consider:

a. one-tailed test

b. two-tailed test

c. one-tailed test because sample proportions are different.

d. two-tailed test because sample size is large.

1b.) Assuming computed Z of 1.04 for the test, what is your conclusion?

a. Reject H0. Proportion of dog owners owning more than one dog has decreased.

b. Fail to reject H0. Proportion of dog owners owning more than one dog has decreased.

c. Reject H0. Proportion of dog owners owning more than one dog has not decreased.

d. Fail to reject H0. Proportion of dog owners owning more than one dog has not decreased.

e. None of the above.

1c.) A Rutgers University professor claims that there is no significant difference between proportion of female (f) and male students (m) of the university who exercise at least 15 minutes a day. What would be a proper conclusion if he collects data, conducts hypothesis test, and finds P-value of 0%.

a. Reject H0. There is a significant difference. --> I THINK THIS IS THE ANSWER BUT I JUST WANT TO KNOW WHY

b. Reject H0. There is no significant difference.

c. Fail to reject H0. There is a significant difference.

d. Fail to reject H0. There is no significant difference.

1d.) A Rutgers University professor claims that female students study more than male students. What would be a proper conclusion if he collects data from random sample of 200 males and sample of 343 females, and finds P-value of 0.65?

a. Reject H0. Female students study more than male students.

b. Fail to reject H0. Female students study more than male students.

c. Fail to reject H0. Female students study less than male students.

d. Fail to reject H0. Female students study almost the same as male students. ---> I THINK THIS IS THE ANSWER I JUST WANT TO KNOW WHY

Answer 1

1.  p1= proportion of dog owners who owned more than one dog in 2010.

p2= proportion of dog owners who owned more than one dog in recent
Null hypothesis, H0 : p1 = p2

Alternate Hypothesis HA : p1 < p2

1A. a. One tail test

1B. Computed Z = 1.04

Critical value at 5%, Z = -1.6449

Since Computed Z does not lie in the critical region ( i.e leaa tha -1.6449) we Fail to reject H0.

  Fail to reject H0. Proportion of dog owners owning more than one dog has not decreased.

1C. Let p(f) - proportion of female who exercise atleast 15 minutes a day

& p( m)- proportion of male who exercise atleast 15 minutes a day.

   Null hypothesis, H0 : p(f) = p(m)

Alternate Hypothesis HA : p(f) not= p(m)

P-value is 0%

As Here Significance level is not given , we will assume 5% is the significance level by default

Since p- value < significance level , so we will reject the null Hypothesis.

Reject H0. There is a significant difference.

1d)  P-Value = 0.65

P-Value > significance level (0.05)

Fail to reject Null hypothesis

  d. Fail to reject H0. Female students study almost the same as male students