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Math
Posted 3 months ago

A city used to require mailed payments for parking tickets. City officials piloted a system that allowed people to choose between paying by mail or paying online. They were curious if giving people both payment options would result in fewer unpaid parking tickets. To test the new system, each parking ticket one month was printed with either a "mail only" payment option or both payment options (mail and online). Officers flipped a coin to determine which message was printed on each ticket.

The data from their study was used to test H0:pB=pMH_{0}: p_{\mathrm{B}}=p_{\mathrm{M}} versus Ha:pB<pMH_{\mathrm{a}}: p_{\mathrm{B}}<p_{\mathrm{M}}, where pBp_{\mathrm{B}} is the proportion of unpaid tickets with both payment options and pMp_{\mathrm{M}} is the proportion of unpaid tickets with the mail only option. The results of the study produced a test statistic of z=2.90z=-2.90 and P\mathrm{P}-value of approximately 0.002 . Assume that all conditions for inference were met.

At the α=0.01\alpha=0.01 level of significance, is there sufficient evidence to conclude that the proportion of unpaid tickets is lower when both payment options are offered?

Choose 1 answer:
(A) Yes, since the PP-value is less than 0.01 .
(B) Yes, since the test statistic is less than 0.01 .
(c) No, since the P-value is less than 0.01 .
(D) No, since the test statistic is less than 0.01 .
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Answer from Sia
Posted 3 months ago
Solution by Steps
step 2
The PP-value of 0.002 is less than the significance level α\alpha of 0.01
step 3
Since the PP-value is less than α\alpha, we reject the null hypothesis H0H_0
step 4
By rejecting H0H_0, we have sufficient evidence to support the alternative hypothesis HaH_a
A
Key Concept
Hypothesis Testing and P-value
Explanation
In hypothesis testing, if the PP-value is less than the significance level α\alpha, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

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