What are the political affiliations of first-year college students? A political scientist claims that 44% of first-year collegestudents characterize themselves as being "moderate" or "middle of the road" (as opposed to being liberal or conservative). You believe this claimed value is too high. You survey a random sample of 525 first-year college students and find that 206 characterizethemselves as being "moderate" or "middle of the road."

1. We always begin a hypothesis test with the claim being tested. Here that claim (using appropriate symbols) is Ho:p= 0.44. We call this the __________________ hypothesis.

2.Look back the hypothesis written in Question 1. What does the symbol "p" stand for?

1. Remember that with hypothesis testing, we always begin with a set of competing hypotheses. This means, in addition to a hypothesis about the claim being tested (from Question 1), we need a hypothesis that illustrates what we think is really going on. In this particular example, using appropriate symbols, we would show this hypothesis as: Ha:p< 0.44. We call this the ______________________hypothesis.
2. Look carefully at the hypothesis given in Question 3. Why is a "<" (or less than) signbeing used in that hypothesis?
3. Given that 206 out of a sample of 525 first-year students identified themselves as being"moderate" or "middle of the road,"what will the sample proportion (or?) be? Please compute this value below and round your answer to three decimal places.
4. To be able to conduct a hypothesis test, we will now need to compute atest statistic(using the following formula). Please attempt to compute this test statistic below, showing as much work as you can.
5. ?=
6. ?(1 ?)
7. ?
8. Based on the test statistic you calculated to answer Question 6, what should thep-valuebe equal to? Please use Table B to find this p-value.

? ?

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1. Remember we determine if we should reject the null hypothesis based on how thep-value compares to our chosen significance level. If we assume here that we are using a significance level (or an alpha level) of 0.05, should we reject the null hypothesis or fail to reject the null hypothesis? Please explain the reason for your answer.
2. If a smaller significance level had been chosenlike 0.01would you have made a different decision (compared to the decision you explained in your answer to Question 8) about whether to reject or fail to reject the null hypothesis? Please explain.

Now that you've had a chance to reason through a hypothesis testing problem from start to finish, let's attempt to solidify someof the big ideas with a new problem.

10. It is claimed that 68% of college students change their majors at least once. A researcher believes this claimed value is too low. He surveys a random sample of 247 college students and finds that 72% of them have changed their majors at least one time. Use this information to conduct a hypothesis test at a significance (or alpha) level of 0.05.

A. What will the hypotheses be? Ho:

Ha:

1. Calculate the test statistic below.
2. Based on what you see in Table B, what should thep-value be?

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D. Will you reject or fail to reject the null hypothesis? Please state your decision and the reason why you are making that decision.

11. A claim is made that 20% of golfers are left-handed. You dispute this claim and gather data from a random sample of golfers in order to test the claim. write out your null hypothesis as follows. What is incorrect about this hypothesis?

Ho:?= 0.20

1. It is claimed that 40% of dog owners have at least two dogs. A researcher believes that claimed value is too high. A random sample of data is gathered in order to conduct a hypothesis test, and ap-value of 0.2420 is obtained. The researcher concludes that the null hypothesis should be rejected since thep-value is smaller than 0.40. What is wrong with this conclusion?
2. A claim is made that 15% of college students major in Business. You believe that more than 15% major in Business. You intend to gather a random sample of data to conduct a hypothesis test, and you begin by stating the null hypothesis and alternative hypothesis. What is wrong with the hypotheses shown below?
3. Ho:p>0.15 Ha:p=0.15

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14. A claim is made that 85% of college students own a smartphone. Ethan believes that a larger percentage of college students own smartphones. He surveys a random sample of 100 college students, and he finds that 90% of these students own a smartphone. The calculations Ethan engaged in to determine the test statistic are shown below. What iswrong with Ethan's calculations?

?=0.850.90= 1.7

_____________________

0.90 (1 0.90) 100