Stats Math

Math 10 MPS - Homework 7 1. The geyser Old Faithful in Yellowstone National Park is claimed to erupt for on average for about three

minutes. Thirty-six observations of eruptions of the Old Faithful were recorded (time in minutes)

1.8 1.98 2.37 3.78 4.3 4.53 1.82 2.03 2.82 3.83 4.3 4.55 1.88 2.05 3.13 3.87 4.43 4.6 1.9 2.13 3.27 3.88 4.43 4.6

1.92 2.3 3.65 4.1 4.47 4.63 1.93 2.35 3.7 4.27 4.47 6.13

Sample mean = 3.394 minutes. Sample standard deviation = 1.168 minutes

Test the hypothesis that the mean length of time for an eruption is 3 minutes answering ALL the following questions:

A. General Question a. Why do you think this test is being conducted?

B. Design

a. State the null and alternative hypotheses b. What is the appropriate test statistic/model? c. What is significance level of the test? d. What is the decision rule?

C. Power Analysis Suppose you wanted to conduct a Power analysis if the population mean under Ha was actually 3.3 minutes. Use the online Power calculator to answer the following questions.

a. Determine the Power of the test using the online power calculator. b. Determine Beta. c. Determine the sample size needed if you wanted to conduct the test in Question with 95% power.

D. Conduct the test a. Are there any unusual observations that question the integrity of the data or the

assumptions of the model? (additional problem only) b. Is the decision to reject or fail to reject Ho?

E. Conclusions - State a one paragraph conclusion that is consistent with the decision using language that is clearly understood in the context of the problem. Address any potential problems with the sampling methods and address any further research you would conduct.

2. 15 I-pod users were asked how many songs were on their I-pod. Here are the summary statistics of that study:

200650 == sX Can you support the claim that the population standard deviation is under 300? Conduct the test with α= 5% .

Show all steps.

3. Define the following terms:

a. Parameter b. Statistic c. Statistical Inference d. Hypothesis e. Hypothesis Testing f. Null Hypothesis (Ho) g. Alternative Hypothesis (Ha) h. Type I Error i. Type II Error j. Level of Significance (α) k. Beta (β) l. Statistical Model m. Test Statistic n. Model Assumptions o. Critical value(s) p. Rejection Region q. p-value r. Decision Rule s. Power t. Effect Size

4. The drawing shown diagrams a hypothesis test for population mean design under the Null Hypothesis (top drawing) and a specific Alternative Hypothesis (bottom drawing). The sample size for the test is 200.

a. State the Null and Alternative Hypotheses

b. What are the values of μ0 and μa in this problem?

c. What is the significance level of the test?

d. What is the Power of the

test when the population mean = 4?

e. Determine the probability associated with Type I error.

f. Determine the probability

associated with Type II error.

g. Under the Null

Hypothesis, what is the probability the sample mean will be over 6?

h. If the significance level was set at 5%, would the power increase, decrease or stay the same?

i. If the test was conducted, and the p-value was .085, would the decision be Reject or Fail to Reject the Null Hypothesis?

j. If the sample size was changed to 100, would the shaded on area on the bottom (Ha) graph increase, decrease or stay the same?