Consider the following data:

Step 2 of 5:

What are the MAD, MSE and MAPE scores for the three-period moving average? Round any intermediate calculations, if necessary, to no less than six decimal places, and round your final answer to one decimal place.

A nutritionist is interested in determining the percentage of American adults who eat salad at least once a week. She takes a random sample of 200 American adults and finds that 176 of them eat salad at least once a week. Find a 95% confidence interval for the true proportion of American adults who eat salad at least once a week. Due to the different methods, round OUT and give 2 decimal places. Select the best possible answer.

In 4 sentences, explain when would be appropriate to choose the following tests? [Hint: type of variables involved, information the test provides] (2 pts each)

a) Chi-squared test

b) Kaplan-Meier Survival Curve

c) Correlation Analysis

d) Logistic Regression

e)Tukey’s HSD with ANOVA

Q1. Consider the population of adult females resident in Melbourne. Our focus is on the population mean height. Assume we know ? (population standard deviation) is 25, but we do not know the population mean, µ. We take a sample of adult females resident in Melbourne (n=100) and calculate the sample mean height as 70 cm.

i) Write down the distribution of X, female height.

ii) Write down the distribution of Are you relying on any theorems in your answer? If yes explain.

iii) Derive the 95% confidence interval around the sample mean. In your answer to iii) will the specific confidence interval you have derived contain the population mean? Explain carefully

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for p is 0.31

(b) there is no preliminary estimate for p

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of medical files is used to estimate the proportion p of all people who have blood type B.

If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p̂ will be within a distance of 0.06 from p? (Round your answer up to the nearest whole number.)

____________medical files

Answer part (a) if you use the preliminary estimate that about 12 out of 90 people have blood type B.

_____________medical files

A new drug cures 70 ​% of the patients to whom it is administered. It is given to 28 patients. Find the probabilities that among these​ patients, the following results occur. Use the normal distribution approximation to the binomial distribution.

​(a) Exactly 22 are cured.

​(b) All are cured.

​(c) No one is cured.

​(d)14 or fewer are cured.

The regression equation is always the best predictor of a y-value for a given value of x. Defend your answer.

Consider a  two-sample t-test.

1. Why is the sign of the t-test arbitrary? .

2. 2. Why are the degrees of freedom associated with the dependent groups t-test always smaller than the degrees of freedom for the independent groups t-test? Be sure to illustrate the calculation of each type of df.

   3. Describe how one would test the homogeneity of variance in a two-sample t-test. How is this information used in your hypothesis testing?

   4. How would you go about using a confidence interval to illustrate a statistically significant difference (or lack thereof) between two groups?

Blind Spot Lab: What percent of the mean is the standard deviation?

- The percentages were 73% and 90%. What does this mean in reference to variability?

A pharmaceutical company tested four formulations of a pain relief medicine for migraine headache sufferers. For the experiment, 32 volunteers were selected and 8 were randomly assigned to one of four drug formulations. The subjects were instructed to take the drug during their next migraine headache episode and to report the time it needs for their pain to go away after taking the drug. Carry out an appropriate test to see if there are any mean differences in pain relief time (in minutes) among the four drug formulations. Calculate the mean squares for treatments (MS_T), the mean squares for error (MS_E), and the value of the test statistic (or the F-ratio). The ANOVA table is listed below.

Analysis of Variance

1. Identify the type of test (chi-square, t-test, or ANOVA) that we have to use in each of the following scenarios. Explain why you chose that test.
   1. We want to compare males and females (gender) based on the difference in time spent on social media (measured as hours per day)

2. We want to compare our customers and the customers of our closest competitors based on their brand loyalty (measured as a Likert scale from 1 to 5)

• 3. We want to compare resident and commuter students based on differences in their gender (males and females)

4. We want to compare freshmen, sophomores, juniors, and seniors based on differences in time spent studying (hours per day)

5. We want to compare freshmen, sophomores, juniors, and seniors based on their willingness to recommend their school (simply measured as Yes/No).

6. We want to compare males and females based on their consumption of sugary drinks (ounces per day).

draw statistics decision tree with 15 tests

The Milwaukee Theatre Guild has just received an anonymous $250,000 donation to be used as follows: $7500 block grants to children’s theatre groups, $6000 grants for new playwrights, and $5000 grants for theatre scholarships. The donor has stipulated that at least eight children’s theatre groups must be funded. Other than that, the Guild may award the donation any way it sees fit. The Guild has determined the following goals:

1. Award at least 40 block grants (children’s theatre).
2. Give at least 60% of the total funding to education (children’s theatre groups and scholarships).
3. Keep the number of scholarships from exceeding the number of new playwright awards by more than five.
4. Award at least 15 total grants.

Formulate a goal program with the weight of 4 for each detrimental deviation from goal 1, a weight of 3 for every $1000 deviation from goal 2, a weight of 2 for each detrimental deviation from goal 3, and a weight of 1 for each deviation from goal 4. Solve for the recommended allocation of the funds.

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $42,000 and $59,800. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. (Round your answers up to the nearest whole number.)

What is the planning value for the population standard deviation?

A. How large a sample should be taken if the desired margin of error is $600?

B. How large a sample should be taken if the desired margin of error is $200?

C. How large a sample should be taken if the desired margin of error is $100?

D. Would you recommend trying to obtain the $100 margin of error? Explain.