# statistic assignment 4

**Answer all questions. Show all calculations. Explain clearly and completely.**

1. A statewide poll for an upcoming gubernatorial election concluded that 52.8% of the voters will vote for candidate A and 47.1% will vote for candidate B. The margin of error is ±2.5%. The confidence level for this result is 95%.

1a. **Explain** the Confidence Interval. (3 pts.)

1b. **Explain** the difference between the Confidence Interval and the Confidence Level. (5 pts.)

1c. **Explain** what happens to the Confidence Level when the Confidence Interval is increased (widened). (4 pts.)

1d. Is the poll result predicting a win for either candidate (A or B)? **Explain**. (5 pts.)

1e. **Explain at least two reasons** that could cause these poll results to be inaccurate,biased or unreliable. (8 pts.)

**2.** A university president claims that on average, at least 60% of incoming freshman students go on to earn their degrees and graduate from the university.

For the hypothesis test, a random sample of 50 freshman students were selected for a sample study. 27 of them graduated with their degrees. 27 out of 50 is 54%.

The test statistic (formula result) is z = -1.46.

The p-value for this test statistic is .0721 or 7.21%.

2a. **Explain** is the parameter of interest? (3 pts)

2b. **Explain** the Null Hypothesis. (4 pts.)

2c. **Explain** the Alternative Hypothesis. (4 pts.)

2d. Based on the test statistic, z, and the p-value, **explain** whether we should accept or reject the Null hypothesis. (6 pts.)

2e. **Explain** in your own words what the conclusion in 2d says about the result of the test and the action to be taken. (8 pts)