CK-12 Probability and Statistics - Advanced

8.2. Testing a Proportion Hypothesis http://www.ck12.org

where:

p=the sample proportion

P=the hypothesized population proportion

sp=the standard error of the proportion

4. We can construct something called the confidence interval that specifies the level of confidence that we have in
   our results. The confidence interval is a range of values that we are confident, but not certain, contains the population
   parameter that we are studying.

Review Questions

1. The test statistic helps us determine ___.


2. True or false: In statistics, we are able to study and make inferences about proportions, or percentages, of a
   population.


3. True or false: A confidence interval states the probability that the interval contains the mean. For example, a
   confidence interval of 95% would say that “This interval contains the mean 95% of the time.”

A state senator cannot decide how to vote on an environmental protection bill. The senator decides to request her
own survey and if the proportion of registered voters supporting the bill exceeds 0.60, she will vote for it. A random
sample of 750 voters is selected and 495 are found to support the bill.

4. What are the null and alternative hypotheses for this problem?


5. What is the observed value of the sample proportion?


6. What is the standard error of the proportion?


7. What is the test statistic for this scenario?


8. What decision would you make about the null hypothesis if you had an alpha level of.01?


9. The state senator decided that she is still wants an estimate of the proportion of voters in the population who
   are likely to vote for the bill. Construct a 99% confidence interval around this proportion.


10. Please write a statement describing the results of the confidence interval.

Review Answers

1. The magnitude of the difference between the observed sample mean and the hypothesized population mean.


2. True


3. False

Wecan notsay that the probability is 95 percent that the interval contains the mean since either the interval contains
the mean or it does not. Therefore, when we talk of our confidence level we say that we are ’X% certain” that the
specific interval contains the mean.

4.H 0 :P= 0. 60 ,Ha:P> 0. 60

5. p= 495 / 750 = 0. 66


6. 
   
   
   
   0. 0179
      7.z= 3. 35
   
   
   
   


7. Since the test statistic of 3.35 is exceeds the critical value of 2.33 (one-tailedz-test at.01), we reject the null
   hypothesis and conclude that the probability is less than 0.01 that a sample proportion of 0.66 would appear
   due to sampling error if in fact the population proportion was equal to 0. 60.