Question

Math

Posted 3 months ago

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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 $H_{0}: p_{\mathrm{B}}=p_{\mathrm{M}}$ versus $H_{\mathrm{a}}: p_{\mathrm{B}}<p_{\mathrm{M}}$, where $p_{\mathrm{B}}$ is the proportion of unpaid tickets with both payment options and $p_{\mathrm{M}}$ is the proportion of unpaid tickets with the mail only option. The results of the study produced a test statistic of $z=-2.90$ and $\mathrm{P}$-value of approximately 0.002 . Assume that all conditions for inference were met.
At the $\alpha=0.01$ 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 $P$-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 $P$-value of 0.002 is less than the significance level $\alpha$ of 0.01

step 3

Since the $P$-value is less than $\alpha$, we reject the null hypothesis $H_0$

step 4

By rejecting $H_0$, we have sufficient evidence to support the alternative hypothesis $H_a$

A

Key Concept

Hypothesis Testing and P-value

Explanation

In hypothesis testing, if the $P$-value is less than the significance level $\alpha$, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

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