11C/D

Number of complaints due to identity theft (out of 500) Value of , the sample proportion P-value Do you think we have convincing evidence to suggest that Florida is exceeding the national trend? Why?
148 0.296 0.098 0.461 No, because a sample proportion of 0.296 is not that unlikely given the national trend of 0.294.
150
155
160
165
170
  P-value Reject or Do not reject the null hypothesis
7) 0.01
8) 0.11
9) 0.50
When the alternative is: The P-value is: The P-value equals:
4) Lower-tailed

(  null value)

 How “unlikely” it is that we observed the sample data that resulted in a test statistic of or lower.

The area on the left of the test statistic under the standard normal curve.
5) Upper-tailed

(  null value)

 How “unlikely” it is that we observed the sample data that resulted in a test statistic of or higher.

The area on the right side of the test statistic under the standard normal curve.
6) Two-tailed

(  null value)

 How “unlikely” it is that we observed the sample data that resulted in a test statistic of or lower OR or higher.

The area on the right of the absolute value of the test statistic and the area on the left of the negative absolute value of the test statistic (i.e., more extreme).
Number of complaints due to identity theft (out of 500) Value of , the sample proportion P-value Do you think we have convincing evidence to suggest that Florida is exceeding the national trend? Why?
148 0.296 0.461 No, because a sample proportion of 0.296 is not that unlikely given the national trend of 0.294.
150 0.3 0.29 0.3859 No, because a sample proportion of 0.30 is not that unlikely given the national trend of 0.294.
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Describe what a P–value measures. 2–6
Identify how a P-value is represented in a statistical distribution. 4–6

The number 123.4567. The one is labeled “hundreds,” the two is labeled “tens,” the three is labeled “ones,” the 4 is labeled “tenths,” the five is labeled “hundredths,” the 6 is labeled “thousandths,” and the 7 is labeled “hundred thousandths.” A graph titled “Figure 4. Flu Vaccination Coverage by Age Group, Adults 18 years and older, United Sates, 2010-2020.” It shows separate dots and lines for “18-49 years,” “50-64” years, “65+ years,” and “Overall.” A number line labeled 0 at one end and 1 at the other end. Someone in a business suit holding up a piece of paper that reads “Consumer Protection.”

Company A P-value = 0.021 “At the 5% significance level, the data provide convincing evidence that more than half of single people believe that online dating is right for them.”
Company B P-value = 0.063 “At the 5% significance level, the data do not provide convincing evidence that more than half of single people believe that online dating is right for them.”
Decision Conclusion
If P-value , there is enough evidence to reject the null hypothesis. At the  100% significance level, the data provide convincing evidence in support of the alternative hypothesis.
If P-value, there is not enough evidence to reject the null hypothesis. At the 100% significance level, the data do not provide convincing evidence in support of the alternative hypothesis.
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Write the conclusion of a hypothesis test in context. 1, Parts B and D

3, Part G
Conduct a complete hypothesis test for a proportion. 3
Understand that there are limitations on P-values.

 

 4
Verify that the conditions of the one-sample z-test for proportions have been met. 2

3, Part C

A glass of water

Glossary 11C

percent
out of one hundred.
significance level
the cut-off for P-values at which we have enough evidence to reject the null hypothesis.
P-value
the probability of obtaining a test statistic at least as extreme (in the direction of the alternative hypothesis) as the one that is actually seen if the null hypothesis is true.