It is believed that standardized test scores, such as SAT, is a good predictor of first-year college students' GPA. x 1200 1120 1000 1420 1280 750 1100 y 3.2 2.5 2.7 3.5 2.9 2.2 2.3 1. Find the the correlation coefficient. Round your final answer to four decimal places. r = 2. Write the regression equation below. Round all numbers to four decimal places. ˆ y = 3. Using the data shown above, predict a student's first-year GPA when the student scores a 1275 on the SAT. Round your final answer to two decimal places. 4. What percentage of variation in GPAs can be explained by students' SAT scores? Round your final answer to two decimal places. %

Find a value of the standard normal random variable z ​, call it z 0​, such that the following probabilities are satisfied.

a. ​P(z less than or equals z 0​) equals 0.3027

b. ​P(minus z 0less than or equals z less than z 0​) equals 0.1518

c. ​P(z less than or equals z 0​) equals0.7659

d. ​P(z 0 less than or equals z less than or equals​ 0) equals 0.2706

e. ​P( minus z 0 less than or equals z less than z 0​) equals 0.8146

f. ​P(minus1less than z less than z 0​) equals 0.5757

Suppose x is a normally distributed random variable with mu equals 43 and sigma equals 5. Find a value x 0 of the random variable x that satisfies the following equations or statements. a. ​P(x less than or equals x 0​)equals0.8413 b. ​P(x greater thanx 0​)equals0.025 c. ​P(x greater thanx 0​) equals 0.95 d.​ P(28 less than or equals x less thanx 0​) equals 0.8630 e.​ 10% of the values of x are less than x 0. f.​ 1% of the values of x are greater than x 0.

Each year about 1500 students take the introductory statistics course at a large university. This year scores on the final exam are distributed with a median of 74 points, a mean of 70 points, and a standard deviation of 10 points. There are no students who scored above 100 (the maximum score attainable on the final) but a few students scored below 20 points. a.Is the distribution of scores on this final exam symmetric, right skewed, or left skewed? b.Would you expect most students to have scored above or below 70 points? c.What is the probability that the average score for a random sample of 40 students is above 75? (please round to four decimal places) Additionally, can this question be answered using excel or statcrunch?

Introduction:

Find a list of at least five related numbers. Compute statistics about the data, and give your interpretation.

Prompt:

Analyze the data you have gathered.

1. Possible sources include the 2010 census, Yahoo finance, and U. S. News and World Report.
2. The data could be sports scores, the national debt, a rate or an amount, such as mortality, literacy, abortion, marriage, high school graduation, college graduation, poverty, income, intelligence quotient, profitability, stock price, dividend, population, or something else. Make sure your list is not the same as another student's.
3. List the data.
4. List your sources.
5. List the statistics you have computed about the data including mean, mode, median, midrange, range, and standard deviation.
6. Give your interpretation of the statistics.

Explain thoroughly the distinctions between the following pairs of terms:

(a) Parameter and statistic

(b) Sample size and number of samples

. Develop a simple linear regression model to predict a person’s income (INCOME) based upon their years of education (EDUC) using a 95% level of confidence.

a. Write the reqression equation.

b. Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.

c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.

d. Interpret the coefficient for the independent variable.

e. What percentage of the observed variation in income is explained by the model?

f. Predict the value of a person’s income using this regression model with 16 years of education.

2. Develop a simple linear regression model to predict a person’s income (INCOME) based on their age (AGE) using a 95% level of confidence.

a. Write the reqression equation.

b. Discuss the statistical significance of the model as whole using the appropriate regression statistic at a 95% level of confidence.

c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.

d. Interpret the coefficient for the independent variable.

What percentage of the observed variation in a person’s income is explained by the model?

e. Predict the value of a person’s income who is 45 years old, using this regression model.

3. Develop a simple linear regression model to predict a person’s income (INCOME) based upon the hours worked per week of the respondent (HRS1) using a 95% level of confidence.

a. Write the reqression equation.

b. Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.

c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.

d. Interpret the coefficient for the independent variable.

e. What percentage of the observed variation in income is explained by the model?

f. Predict the value of a person’s income who works 50 hours a week, using this regression model.

4. Develop a simple linear regression model to predict a person’s income (INCOME) based upon the number of children (CHILDS) using a 95% level of confidence. Children are expensive, and may encourage a parent to earn more to support the family.

a. Write the reqression equation.

b. Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.

c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.

d. Interpret the coefficient for the independent variable.

e. What percentage of the observed variation in income is explained by the model?

f. Predict the value of a person’s income with 3 children, using this regression model..

5. Compare the preceding four simple linear regression models to determine which model is the preferred model. Use the Significance F values, p-values for independent variable coefficients, R-squared or Adjusted R-squared values (as appropriate), and standard errors to explain your selection.

6. Calculate the predicted income of a 45 year old, with 18 years of education, 2 children, and works 40 hours per week using your preferred regression model from part 5.

The breaking strength of yarn used in the manufacture of woven carpet material is Normally distributed with σ = 2.4 psi. A random sample of 16 specimens of yarn from a production run was measured for breaking strength, and based on the mean of the sample (x bar), a confidence interval was found to be (128.7, 131.3). What is the confidence level, C, of this interval?

Please show work and explain

A. 0.95

B. 0.99

C. 0.90

D. 0.97

E. it can not be determined with the info provided

1.

A sample of customers in a grocery store were asked the amount they spent at the grocery store and the number of household members for whom they currently shopped. The results are summarized in the table below:

Find the correlation coefficient for the number of household members versus the dollar amount spent on groceries and round this result to the hundredths place.

2.

Given a trendline of y = 5987x + 143960, where the variable x represents the age of a home (in years) and the variable y represents its current market value (in dollars), use this trendline to predict the current market value of an 8-year old home.  

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data. x: 16 0 13 17 11 23 20 −8 −11 −24 y: 11 −5 26 15 19 28 27 −11 −6 −7 (a) Compute Σx, Σx2, Σy, Σy2. Σx 57 Correct: Your answer is correct. Σx2 Incorrect: Your answer is incorrect. Σy 97 Correct: Your answer is correct. Σy2 Incorrect: Your answer is incorrect. (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to two decimal places.) x y x s2 s (c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.) x y Lower Limit Upper Limit Use the intervals to compare the two funds. 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund. 75% of the returns for the stock fund fall within a narrower range than those of the balanced fund. 25% of the returns for the balanced fund fall within a narrower range than those of the stock fund. 25% of the returns for the stock fund fall within a wider range than those of the balanced fund.

In a survey, people were asked to "randomly pick a whole number between 1 and 20" Here are the responses
3   3   3   4   4   5   7   7   7   8   11   12  
13   13   13   13   13   15   15   16   17   17   17   17
17   17   17   18   19   29
Compute the
mean
median
mode
standard deviation
Q1
Q3
IQR
Based on the mean and median describe the shape of the data:

create a graph of the data and describe the shape of data in a sentence

(a) How many different committees consisting of 3 males and 4 females can be chosen from a group of 8 males and 7 females?

(b) In how many ways can 5 essays be ranked in a contest?

(c) A license plate has three letters from 26 letters of an alphabet and four digits from 0,1,2,3,4,5,6,7,8,9. How many plates can be made if:

i) letters and numbers cannot be repeated?

ii) repetitions are allowed?

1. In the following two situations, either stratified random sampling method or cluster sampling method is used.

(1) Identify the sampling method used, and (2) briefly justify your choice.

1. To get an idea of how much detached houses in the city of Vancouver cost these days, Joe went to a real estate web site (like realtor.ca) to get some information. He divided the city of Vancouver into 20 districts or communities; randomly selected 5 of them; and all detached houses (that are listed on the web site) within those 5 districts were chosen.

2. To get an idea of how much detached houses in the city of Vancouver cost these days, Joe went to a real estate web site (like realtor.ca) to get some information. He divided the city of Vancouver into 20 districts or communities; randomly selected 5 detached houses from each district; and the 100 (20 districts times 5 houses per district) detached houses formed the sample.

Note: In practice, geographic factor should not be used to do the stratification. It’s used here only for the sake of illustration.

7. According to the market research firm NPD Group, Americans ate an average of 211 meals in restaurants in 2001. The following data show the number of meals eaten in restaurants as determined from a random sample of Americans in 2014: 212, 128, 197, 344, 143, 79, 180, 313, 57, 200, 161, 320, 90, 224, 266, 284, 231, 322, 200, 173. Using ? = .05, test the hypothesis that the number of meals eaten at restaurants by Americans has not changed since 2001.

1) Identify the null and alternative hypotheses.

2) Set the value for the significance level.

3) Determine the appropriate critical value.

4) Calculate the appropriate test statistic

. 5) Compare the test statistic with the critical value

. 6) State your conclusion.

7) Calculate and interpret the P-value

2. Bigger sample is not always better – one of the worst statistical mistakes ever made in the history of statistics happened in the 1936 U.S. Presidential Election. The incumbent president Franklin Roosevelt of the Democratic Party and Alf Landon of the Republican Party are the two main presidential candidates. Look the event up at this webpage http://www.math.upenn.edu/~deturck/m170/wk4/lecture/case1.html and answer the following questions.

1. Find the Literary Digest’s pre-election prediction for Roosevelt and Landon, in percentage of popularity vote. (One percentage for Roosevelt and one for Landon.)
2. Find the 1936 Presidential election result for Roosevelt and Landon, in percentage of popularity vote.

(One percentage for each.)

3. Find the sample size used by Literary Digest.
4. The Literary Digest’s sample has a problem with the selection bias. Identify the target population, sampling frame and briefly explain why there was a selection bias.
5. The Literary Digest’s sample also has a problem with the non-response bias. Report the number of surveys sent, number of surveys received, and calculate the non-response rate (in %).
6. The Literary Digest’s sample has a problem with the response bias. Mind you that the US is in their eighth year of the Great Depression. Briefly explain how the Great Depression has anything to do with the response bias.
7. Find the sample size used by George Gallop.
8. What was his (George Gallup’s) pre-election prediction for Roosevelt, in percentage of popularity vote? (Please look this question (h) up on the internet. The numbers may vary from different sources or web sites. Just pick one and it will not be marked based on the accuracy of the numbers.)