A sample of 17 observations is selected from a normal population. The sample standard deviation is 21.75, and the sample mean is 36.

a. Determine the standard error of the mean. (Round the final answer to 4 decimal places.)

The standard error of the mean is            .

b. Determine the 80% confidence interval for the population mean. (Round the final answers to 2 decimal places.)

The 80% confidence interval for the population mean is between  and  .

c. f you wanted a wider interval, would you increase or decrease the confidence level?

(Click to select)  Increase  Decrease

2. Assume you conducted a logistic regression analysis. To analyze the relationship resting heart rate and having a heart attack (heart attack is a dummy variable, 0 = no heart attack, 1 = heart attack). Resting heart rate is the predictor variable and heart attack is the outcome. You found that the beta coefficient is 1.2 and the R2 value is 0.76.

   1. How would you interpret the beta coefficient?

   2. How would you interpret the R2 value?

   3. Assume that the p-value for the beta coefficient was 0.24. How would this

      change your interpretation?

   4. Assume that the p-value for the beta coefficient was 0.03. How would this

      change your interpretation?

A batch of 10 discs has 3 defective discs. A sample of 5 discs is randomly selected from the batch.

A. Find the probability that exactly one disc in the sample is defective.

B. Find the probability that at least 4 discs in the sample are not defective.

1.In a test of the difference in mean incomes of males and females employed in

the same positions p< .20. This means

A. In a t test of the difference between two means you would conclude there is a

difference if alpha=.05

B. In a t test of the difference between two means you would conclude there is a

difference if alpha=.10

C. You would conclude there is a difference only if you were willing to risk a very

large chance of making a Type I error

D. The difference between men and women’s incomes is less than 20%

2. If you conclude that there is no difference in the average achievement test

scores of students in large vs. small classes of the same subject, the probability

that you are making an error is

A. alpha

B. (1- alpha)

C. small if there is only a small difference in the test scores

D. large if the sample size is large

E. large if there is only a small difference in the test scores

3. The probability of determining that there is a difference in the average

achievement scores of students in large vs. small classes of the same subject

when there is no real difference is

A. (1-beta)

B. (1-alpha)

C. beta

D. dependent on your sample size

E. alpha

4. If you measured the average household expenditures on groceries for a

random sample of 50 families in the year 2005 and for those same families again

in 2015 df for a hypothesis test of the difference would be

A. 99

B. 98

C. 50

D. 48

E. 49

5. You want to compare the average number of copies available from two

brands of ink cartridges by comparing the comparing the number of copies from

75 printers using the first brand then replacing those cartridges and determining

the number of copies for those same 75 printers using the second brand. Df

would be

A. 74

B. 148

C. 149

D. 73

E. 150

6. If you were to calculate a confidence interval estimate for the average

difference between the m.p.g. obtained with high octane minus regular gas for a

sample of cars that gave you LCL= (-2) and UCL= 3, you would know

A. the average difference is 5 m.p.g.

B. there may be no difference at all

C. high octane gives you better mileage than regular gas

D. regular gas gives you better mileage than high octane

E. the difference could be as much as 10 m.p.g.

7. If you were to administer a test of short term memory in the form of random

number recall to a random group of 40 adults and calculated their average recall

scores and compared that average to the average recall of a different group of

forty adults who had been engaged in a memory training program, assuming

equal population variances, df would be

A. 80

B. 89

C. 38

D. 39

E. 78

8. A research article investigating the difference between two different

approaches to teaching social skills to autistic adults reports p=.041. You would

conclude

A. There is a difference using alpha=.01

B. There may be no difference using alpha=.05

C. There may be no difference using alpha=.10

D. There is a difference using alpha=.001

E. There is a difference using alpha=.05

9. An F test for equal variances yields p=.377

A. You would do a t test assuming equal variances

B. You would do a t test assuming unequal variances.

10. If the “power” of a statistical test =.80 that means

A. There is a 20% chance of being wrong andrejecting the null when it is true

B. There is a 80% chance you will be right and reject the null when it is false

C. There is a an 80% chance you will be wong and not reject a false null

D. There is a 20% chance you will be right and not reject the null when it is true

E. There is an 80% chance that you will be right in whatever decision you make

Part III: Confidence Intervals for μ (σ known)

9. Suppose IQ scores for adults follow a Normal distribution with a standard deviation of 15. A random sample of 49 adults yields an average score of 100.

a) Construct 90%, 95%, and 99% confidence intervals for μ.

b) What is happening to the width of the confidence intervals as the confidence levels increase?

     Explain why this makes sense both practically and mathematically (based upon the formula).

c) Using the known standard deviation of 15 and confidence level of 95%, construct 3 different  

      confidence intervals based upon sample sizes 49, 100, and 225, respectively.

d) What is happening to the width of the confidence intervals as the sample sizes increase?

     Explain why this makes sense both practically and mathematically (based upon the formula).

A. The percentage of the three different political affiliations of the citizens of the United Kingdom is presented in the table below.

Political Party Percentage

Conservative Party 47%

Labour Party 37%

Other 16%

• A random sample of 200 UK citizens are taken.

A-1) What is the sampling distribution for the sample proportion of UK citizens who support the Conservative Party?

A-2) What is the sampling distribution for the sample proportion of UK citizens who support the Labour Party?

A-3) What is the sampling distribution for the sample proportion of UK citizens who support neither the Conservative nor Labour Party?

A-4) What is the approximate probability that the sample proportion of UK citizens who support the Conservative party is higher than 0.47?

A-5) What is the approximate probability that the sample proportion of UK citizens who support the Labour party is less than 0.30?

A-6) What is the approximate probability that the sample proportion of UK citizens who support neither the Conservative nor Labour Party falls between 0.1 and 0.2?

i will rate

The Environmental Protection Agency (EPA) is concerned about pollution caused by factories that burn sulfur-rich fuel. In order to decrease the impact on the environment, factory chimneys must be high enough to allow pollutants to dissipate over a larger area. Assume that the mean height of chimneys in these factories is 100 meters (an EPA acceptable height) with standard deviation 12 meters. Use the appropriate Excel function to calculate each of the following. (Note – Part (b) will be answered by-hand.) [1 point each]

(b) Write your answer for Part (b) directly on the output. Suppose that the heights of all individual chimneys in the population vary according to an unknown distribution. Suppose that samples of 40 chimneys will be selected and the mean height of each sample, ?̅, will be recorded. What will be the shape of the sampling distribution of the ?̅ values? How do we know this?

(c) Find the probability that the mean height for a sample of 40 chimneys is greater than 102 meters.

(d) Find the probability that the mean height for a sample of 40 chimneys is between 101 and 103 meters.

8. A professor tests whether the loudness of noise during an exam (low, medium, and high) is independent of exam grades (pass, fail). The following table shows the observed frequencies for this test.

Part A) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.)

Decide whether to retain or reject the null hypothesis.

Part B) Compute effect size using Cramer's V. (Round your answer to two decimal places.)

9. What is Cramer's V for each of the following values for the chi-square test for independence? (Round your answers to two decimal places.)

Part A) X² = 3.63, n = 50, df_smaller = 1

Part B) X² = 9.27, n = 120, df_smaller = 2

Part C) X² = 12.23, n = 160, df_smaller = 3

1. What is the danger in using stepwise regression?
2. What is the difference between Cook’s Distance and DFFITS?
3. What can you do to remove multicollinearity?
4. What is a VIF?
5. If you have to create dummy variables for the seven continents of the world, how many columns do you create and why?
6. Why do we standardize residuals?
7. Describe a QQ plot and what it can tell us.

Let’s play a game! It costs you only $10 to play! Roll two dice. If you roll snake eyes (two 1’s), then I’ll give you $500. If you roll anything else, then I’ll give you nothing. Using expected value, decide if you should play this game!

An Izod impact test was performed on 20 specimens of PVC pipe. The obtained standard deviation was s = 0.328. Assume that the random sample was drawn form a normal population N (µ, σ^2 ), with unknown mean value µ and unknown variance σ^2 .

a) Give a 99% confidence interval for the variance σ^2 .

b) Give a 99% upper confidence bound for the variance σ^2 .

c) Test the hypothesis

H0 : σ^2 = 0.1,

against the two-sided alternative

H1 : σ^2 ≠ 0.1,

at the significance level α = 0.01.

d) Explain the connection between your two-sided confidence interval and the significance test.

12.) Facebook reports that 70% of their users are from outside of the United States and that 50% of their users log on to Facebook every day. Suppose 20% of their users are United States users log on every day. a) What percentage of Facebook’s users are from the United States? b) What type of probability is the 20% mentioned above? c) Construct a contingency table showing all the joint and marginal probabilities. d) What is the probability that a user is from the United States given that he or she logs on every day? e) Are From the United States and Log on Every Day independent? Explain 33.) In a sample of real estate ads, 64% of homes for sale had garages, 21% have swimming pools, and 17% have both features. What is the probability that a home for sale has: a) A pool, a garage, or both? b) Neither a pool nor a garage? c) A pool but no garage?  

A machine produces metal rods used in an automobile suspension system. A random sample of n = 12 rods is selected, and their diameters are measured. The resulting data in millimeters are shown here: 8.23 8.31 8.42 8.29 8.19 8.24 8.19 8.29 8.30 8.14 8.32 8.40

a) Calculate the sample mean x bar and the unbiased variance estimate s^2

b) Let α = 0.05. Determine the percentage point tα/2, n−1 of the corresponding t-distribution.

c) Assuming that the data comes from a normal population N (µ, σ^2 ), with unknown mean µ and unknown variance σ^2 , find a 95% two-sided confidence interval on mean value µ of the rod diameter.

d) Test the null hypothesis H0 : µ = µ0 = 8.20 mm,

Suppose that x has a binomial distribution with n = 50 and p = 0.6, so that μ = np = 30 and σ = np(1 − p) = 3.4641. Approximate the following probabilities using the normal approximation with the continuity correction. (Hint: 25 < x < 39 is the same as 26 ≤ x ≤ 38. Round your answers to four decimal places.)

(a) P(x = 30)

(b) P(x = 25) (

c) P(x ≤ 25)

(d) P(25 ≤ x ≤ 39)

(e) P(25 < x < 39)

Requirements:

Moving Averages. Use the below actual sales to calculate a one-year average which will be used as the forecast for next periods (chapter 14, text). Choose a moving average period that best supports this calculation.

Exponential Smoothing. Use the same data to forecast sales for the next periods with α=.40 (chapter 14, text).

Regression Analysis on Excel. Draw a scatter graph from Insert/Graph/Scatter graph selections in Excel (chapter 15, text).

Month Actual Sales

1 3050

2 2980

3 3670

4 2910

5 3340

6 4060

7 4750

8 5510

9 5280

10 5504

11 5810

12 6100