Question

Consider the following two questions designed to assess quantitative literacy.

What is 15% of 1000?
A store is offering a 15% off sale on all TVs. The most popular television is normally priced at $1000. How much money would a customer save on the television during this sale?
Suppose the first question is asked of 200 randomly selected college students, with 168 answering correctly; the second one is asked of a different random sample of 200 college students, resulting in 147 correct responses. Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context. (Use p1 for the true proportion students who answered the question without context correctly and p2 for the true proportion of students who answered the question with context correctly.)
State the relevant hypotheses.
H0: p1 − p2 = 0
Ha: p1 − p2 < 0H0: p1 − p2 = 0
Ha: p1 − p2 ≠ 0 H0: p1 − p2 = 0
Ha: p1 − p2 > 0H0: p1 − p2 < 0
Ha: p1 − p2 = 0H0: p1 − p2 > 0
Ha: p1 − p2 = 0
Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z=P-value=
State the conclusion in the problem context.
Fail to reject H0. The data does not suggest that the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one.Reject H0. The data does not suggest the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one. Fail to reject H0. The data suggests the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one.Reject H0. The data suggests that the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one.
You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

A customer would save $ 150 on the television during this sale and pay

$ 850.

Reject H0. The data suggests that the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one

Explanation:

15% of 1000

=0.15 *1000= $ 150

A customer would save $ 150 on the television during this sale.

p1 = the true proportion students who answered the question without context = 168/200

p2 = the true proportion of students who answered the question with context correctly = 147/200

The null and alternate hypotheses are

H0: p1 − p2 = 0 i.e the true proportion of correct responses to the question without context is the same as that for the one with context

against the claim

Ha: p1 − p2 > 0 that is the true proportion of correct responses to the question without context exceeds that for the one with context

2) The significance level is set at 0.05

3) The critical region is z > ± 1.645

4) The test statistic

Z= p1-p2/ sqrt [pcqc ( 1/n1+ 1/n2)]

Here p1= 168/200= 0.84

and p2= 147/200=0.735

pc = 168+147/200+200

pc= 315/400= 0.7875

qc= 1-pc= 1-0.7875=0.2125

5) Calculations

Z= p1-p2/ sqrt [pcqc ( 1/n1+ 1/n2)]

z= 0.84-0.735/√ 0.7875*0.2125( 1/200+ 1/200)

z= 0.105/0.0409076

z= 2.5667

6) Conclusion

Since the calculated value of z= 2.5667 lies in the critical region the null hypothesis is rejected and it is concluded that the true proportion of correct responses to the question without context exceeds that for the one with context.

The value of z is 2.5668.

The value of p is 0.01016