1. A national poll found that 454 people out of 1000 believe in UFO's.Answer the following questions.

a. what is the point estimate for the number of people who believe in UFO,s?

b. Find the 94% confidence interval for the number of people who believe in UFO's.

c. Give a statement about the confidence interval in the context of the problem.

d. Does this confidence interval provide good evidence that the actual percentage of people who believe in UFO's is 48%?Explain.

e. Suppose we wish to perform a hypothesis test on this poll.Does this provide good evidence that the number of people who believe in UFO's is less than 48%?Perform the test at the 3% significance level.State the hypotheses, find the test statistic and p-value and state the decision.

f. State the conclusion of the above hypothesis test in the context of the problem.

g. The conclusions from d and e agree? Explain.

2.1 Suppose Joe is testing a hypothesis at the 5% significance level.The population mean is 20, and the observed mean is 18.The population standard deviation is 6.The sample size is 25. Joe found that the p-value is 0.054, which led him to not reject the null hypothesis.He was told by his statistics teacher that his answer is incorrect.What is the correct answer, and what did Joe do wrong?

3.1 Here are the lengths in cm of young hellbenders before their release.

20.5 21 24 23.5 20.2 25 19.6 24 18 28 19 24 25.1 23.7 26 16.2 25 22.3 23.6 22

a. The average length of hellbenders ready to release into the wild is 24 cm.You are worried that this sample of hellbenders is, on average, too small to release into the wild.At the 5% significance level, do we have good evidence that these hellbenders are too small?State the hypotheses, find the test statistic and p-value and state the decision.

b. State the decision in the context of the problem.

c. Suppose some of the lengths of the hellbenders were recorded incorrectly, and the true average of the hellbenders was 24 cm.Did you just find a Type I error, a Type II error or make the correct decision?

4.Suppose you wanted to take another sample of hellbenders to find a 95% confidence interval of young hellbenders to release.You know that the population mean of these hellbenders is 24 cm and the population standard deviation is 3 cm.What is the sample size needed to have a .75 margin of error?