# MATHEMATICS

MAT 543 Week 4 Homework

Chapter 5: Exercises 5-1, 5-3, 5-5, and 5-6 (page 87 of the text)

5-1 Indicate the different ways an individual could forecast his or her weight 10 years from now. Do these methods change based upon whether the individual is 5, 14, 24, or 45 years old? If so, why?

5-3 Provide examples from the field of health services management of phenomena that are probably best forecasted using genius forecasting. Why?

5-5 Calculate the expected number of infants needing neonatal intensive care in a hospital if the historic rate is 5 per 1000 births, and you expect 575 births this year.

5-6 If the annual death rate from smoking is 154 deaths per 100,000 persons, and the annual death rate from firearms is 13.5 deaths per 100,000 persons, how many deaths from these causes would you expect in a community of 1 million people?

1. Describe the properties of a Student’s t distribution, e.g. shape of distribution and degrees of freedom.

2. Discuss the connections between a confidence level, margin of error, and the critical values.

3. A 90% confidence interval for the mean of a given population is computed from a random sample and found to be .

Based on this information, which of the following statements is true about this confidence interval?

Select one:

a. There is a 90% probability that is between 8 and 16.

b. All of the above statements about confidence intervals are true.

c. There is a 90% confidence that the true mean of the population is between 8 and 16.

d. 90% of the values sampled are between 8 and 16.

e. There is a 90% probability that the true mean of the population is 12 and a 90% probability that the true margin of error is 3.

4. As the margin of error of a confidence interval increases, ___.

Select one:

a. the sample mean increases.

b. the population standard deviation increases.

c. the confidence interval decreases.

d. the population standard deviation decreases.

5. Based on the statement, “We are fairly sure that this new drug can eliminate headaches. Let’s put it on the market,” you have created the following null and alternative hypotheses:

H0: The drug does not eliminate headaches.

Ha: The drug does eliminate headaches.

Which of the following is the Type I error associated with this scenario?

Select one:

a. We conclude that the drug does not eliminate headaches and it really does not

b. We conclude that the drug does not eliminate headaches when it really does

c. We conclude that the drug eliminates headaches and it really does

d. We conclude that the drug eliminates headaches when it really does not

6.Based on the statement, “We are fairly sure that this new drug can eliminate headaches. Let’s put it on the market,” you have created the following null and alternative hypotheses:

H0: The drug does not eliminate headaches.

Ha: The drug does eliminate headaches.

Which of the following is the Type II error associated with this scenario?

Select one:

a. We conclude that the drug does not eliminate headaches and it really does not

b. We conclude that the drug does not eliminate headaches when it really does

c. We conclude that the drug eliminates headaches when it really does not

d. We conclude that the drug eliminates headaches and it really does

7. In a hypothesis test, assuming the null hypothesis is true, the probability that the test statistic will take a value at least as extreme as the value actually observed is ___.

Select one:

a. the critical value of the test.

b. the level of significance of the test.

c. the p-value of the test.

d. the margin of error of the test

8.In hypothesis testing, the p-value tells us the ____ level of significance at which the null hypothesis can be ____.

Select one:

a. largest; accepted

b. smallest; rejected

c. smallest; accepted

d. largest; rejected

9. In hypothesis testing, which of the following would be strong evidence against the null hypothesis?

Select one:

a. obtaining data with a large p-value

b. obtaining data with a small p-value

c. using a large significance level

d. using a small significance level

e. none of the above is strong evidence against the null hypothesis

10. Which of the following statements about rejecting the null hypothesis is true?

Select one:

a. If the sample data is such that for a one-tailed test of the mean you can reject H0 at the 5% level of significance, you can always reject H0

for a two-tailed test at the 1% level of significance.

Use the following scenario to answer questions #9 and #10.

Based on the statement, “We are fairly sure that this new drug can eliminate headaches. Let’s put it on the market,” you have created the following null and alternative hypotheses:

H0: The drug does not eliminate headaches.

Ha: The drug does eliminate headaches.

b. If the sample data is such that for a one-tailed test of the mean you can reject H0

at the 1% level of significance, you can always reject H0 for a two-tailed test at the same level of significance.

c. If the p-value is such that you can reject H0 for a 1% level of significance, you can always reject it for a 5% level of significance.

d. If the p-value is such that you can reject H0 for a 5% level of significance, you can always reject it for a 1% level of significance.