Essay(2 Paragraphs)What statistical concept/technique do you think will be the most helpful for you in your future? Please specifically identify and describe one concept or technique and explain how y

Essay(2 Paragraphs)

What statistical concept/technique do you think will be the most helpful for you in your future? Please specifically identify and describe one concept or technique and explain how you think it will be helpful to you.

Review

1. It appears that new car purchases have peaked in 2018 vs. used car purchases. The following probability distribution table shows the random variable x, where x is the number of new cars purchased by household during the last five years:

x

P(x)

0

0.15

1

0.25

2

0.45

3

0.14

4

0.01

a. What is the mean of x (round to 2 decimal places)

b. What is the standard deviation of x

2. In a Sunday baseball league, Mike Kulansky had a 0.500 probability of hitting safely. Assume he had 8 bats in one game.

a. Let X be the number of hits Mike got. The distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q).

b. Find the probability that he gets at least 5 hits in one game (round to 3 decimals)

3. Assume that gas mileage for cars is normally distributed with a mean of 25 miles per gallon and a standard deviation of 10 miles per gallon.

a. What is the probability that a randomly selected car gets between 22 and 28 miles per gallon? (round to 4 decimals)

b. Find the 90th percentile of the miles per gallon distribution (round to 2 decimals)

4. A psychologist is evaluating different therapies for treating depression. The psychologist selects 100 clients and randomly assigns 25 to each group. After 8 weeks of treatment a depression inventory is administered. Which statistical approach should be used?

a. confidence interval

b. t-test

c. ANOVA

d. Chi square

5. BGE has electricity savings days where it gives back to its customers a percentage of its savings for using less electricity than normal. Before going with this program for the entire state of Maryland, BGE tested this concept using 100 single family households during the month of July when the temperature was predicted to exceed 90 degrees. 50 families were asked to conserve energy but got no monetary incentives. The other 50 families were asked to conserve energy but were offered additional menetary incentives. At the end of July the total energy usage was measured. What would be the appropriate hypothesis test to use to see if monetary incentives would reduce energy consumption?

a. t-test for two independent variable

b. t-test for dependent samples

c. z-test for population mean

d. correlation

e. none of the above

6. According to GEICO less than 25% of auto accidents involve teenagers. According to Maryland records 100 of 500 auto accidents involved teenagers. Using a 0.05 significance level, answer the following:

a. What is the appropriate hypothesis test to do this analysis?

b. What is the null hypothesis and the alternative hypothesis?

c. What is the test statistic ((two decimal places)?

d. What is the p-value (3 decimal places) ?

e. Compare the p-value and the signifcance level alpha (reject or fail to reject)

f. Do the results support Geico's claim? 

7. A business analyst in the Washington, D.C. area looked at the following Christmas 2016 and 2017 toy sales in Metro D.C. Six toy stores were were contacted and shared the following information where x is 2016 sales and y represents 2017 

x (in dollars)

y (in dollars)

10,000

11,500

5000

4500

7500

8500

12,500

13,000

8500

8300

5500

4800

a. find an equation of the least squares regression line with the slope and y-intercept rounded to 2 decimal places

b. Using (a) with a 2016 December holiday sales of $6000, what is the predicted 2017 December holiday sales?

c. for a 2016 sales number of $25,000, the 2017 December prediction would be?

d. What would be your guess for 2018 Christmas sales with everything we talked about in our class? 

8. According to the latest poll, 750 adult respondents believe in global warming. Construct a 95% confidence interval estimate of the proportion of adults who believe in global warming. Round your lower bound and upper bound of the confidence interval to 3 decimal places.

9. Based on the performance of all individuals who took the GRE Verbal Reasoning Exam for the last three academic years, test takers had a mean score of 150 and a standard deviation of 8.5

a. For a sample size of 100, state the standard deviation of the sample mean (standard error of the mean) to 3 decimal places.

b. Find the probability that the sample mean scores is more than 155 (rounded to 3 decimal places)

10. Does an exercise program lower cholesterol? 100 adults were given a weekly exercise program. Cholesterol levels were measured before and after this treatment. the changes in their LDL cholesterol (mg/dL) have a mean of 6 and a standard deviation of 4.

Construct a 90% interval estimate of the mean change in LDL cholesterol after treatment. Round lower and upper bound of the confidence interval to 2 decimal places. Show your work.