The average IQ in America is 100. A researcher wants to test the hypothesis that left-handed individuals have different IQs than the average American. He administers an IQ test to 8 left-handed individuals. They have mean 97.4 with a standard deviation of 13.

Test the hypothesis (=.05) that left handed individuals have different IQs than the average Ameican.

BE SURE TO ANSWER ALL PARTS OF THE QUESTION AND SHOW YOUR WORK WHEN YOU CAN.

a) What is the appropriate test?

b) State the null Hypothesis (in words and with means).

c) State the alternative hypothesis (in words and with means).

d) Find the critical value.

e) Calculate the obtained statistic.

f) Report the results. Make a decision.

g) What does your decision mean?

Third, the researcher wishes to use numerical descriptive measures to summarize the data on each of the two variables: hours worked per week and income earned per year.

b. Compute the correlation coefficient using the relevant Excel function to measure the direction and strength of the linear relationship between the two variables. Display and interpret the correlation value.     

Data for HOURSWORKED63 Excel spreadsheet is below:

Adults around the world watch on average 4 hours of TV a day. A researcher thinks that Americans watch less TV than the international average. He finds 25 Americans who watch 3 hours of television a day on average, with a standard deviation of 2 hours. Using an Alpha = .05, test this hypothesis.

BE SURE TO ANSWER ALL PARTS OF THE QUESTION AND SHOW YOUR WORK WHEN YOU CAN.

a) What is the appropriate test?

b) State the null Hypothesis (in words and with means).

c) State the alternative hypothesis (in words and with means).

d) Find the critical value.

e) Calculate the obtained statistic.

f) Report the results. Make a decision

Third, the researcher wishes to use numerical descriptive measures to summarize the data on each of the two variables: hours worked per week and income earned per year.

(a) Prepare and display a numerical summary report for each of the two variables including summary measures such as mean, median, range, variance, standard deviation, smallest and largest values and the three quartiles.

Notes: Use QUARTILE.EXC command to generate the three quartiles.

Data for HOURSWORKED63 Excel spreadsheet is below:

A company claims that a new manufacturing process changes the mean amount of aluminum needed for cans and therefore changes the weight. Independent random samples of aluminum cans made by the old process and the new process are taken. The summary statistics are given below. Is their evidence the 5% significance level (or 95 confidence level) to support the claim that the mean weight for all old cans is different than the mean weight for all new cans ?Justify fully!

The old process had a sample size of 25 with a mean of 0.509 and a standard deviation of 0.019. The new process has a sample size of 25 with a mean of 0.495 and a standard deviation of 0.021.

For any Hypothesis Test make sure to state Ho, Ha, Test statistic, p-value, whether you reject Ho, and your conclusion in the words of the claim.

For any confidence interval make sure that you interpret the interval in context, in addition to using it for inference.

Second, the researcher wishes to use graphical descriptive methods to present summaries of the data on each of the two variables: hours worked per week and income earned per year, as stored in HOURSWORKED63 worksheet.

(a) The number of observations (n) is 63 individuals. The researcher suggests using 7 class intervals to construct a histogram for each variable. Explain how the researcher would have decided on the number of class intervals (K) as 7.

Data of HOURSWORKED63 Excel spraedsheet is below:

Calculate the t-test statistic for whether the correlation coefficient between the two variables below differs significantly from 0. (Hint: You will first need to calculate the correlation coefficient.)

14        15

17        18

19        13

21        2

23        4

11        5

9          3

13        15

14        18

21        2

1) The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider waits less than two minutes?

A) 0.4706

B) 0.5294

C) 0.6000

D) 0.7059

2) For any normally distributed random variable with mean μ and standard deviation σ, the percent of the observations that fall between [μ - 2σ, μ + 2σ] is the closest to ________.

A) 68%

B) 68.26%

C) 95%

D) 99.73%

3) Which of the following can be represented by a continuous random variable?

A) The time of a flight between Chicago and New York

B) The number of defective light bulbs in a sample of five

C) The number of arrivals to a drive-through bank window in a four-hour period

D) The score of a randomly selected student on a five-question multiple-choice quiz

4) An analyst believes that a stock's return depends on the state of the economy, for which she has estimated the following probabilities:

According to the analyst's estimates, the expected return of the stock is ________.

A) 7.8%

B) 11.4%

C) 11.7%

D) 13.0%

5) How would you characterize a consumer who is risk loving?

A) A consumer who may accept a risky prospect even if the expected gain is negative.

B) A consumer who demands a positive expected gain as compensation for taking risk.

C) A consumer who completely ignores risk and makes his or her decisions solely on the basis of expected values.

D) None of the above.

An agent for a residential real estate company has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage, to predict the monthly rental cost. The agent selects a sample 48 one-bedroom apartments and collects and stores a data in dataset RentSilverSpring (can be found in both editions of datasets on the Blackboard). 7. At the 0.05 level of significance, is there an evidence of a linear relationship between the size of the apartment and the monthly rent? 8. Construct a 95% confidence interval estimate of the population slope. 9. Construct a 95% confidence interval estimate of the mean monthly rental for all onebedroom apartments that have 800 square feet in size. 10. Construct a 95% prediction interval of the monthly rental for an individual one-bedroom apartment that is 800 square feet in size

In a box of 5 balls, 2 are red and 3 are blue. Two balls are randomly selected (without replacement). Let X be the number of red balls in the two selected balls.

a. Find the probability distribution of X (i.e., list all possible values of X and their corresponding probabilities).

b. Find the expected value and the standard deviation of X.

the visit of a customer at a restaurant follows a Poisson process with a rate of 3 arrivals per week. A day with no visits to the restaurant is called a risky day.

a. Find the expected number of risky days in a week

b.  Given that a risky day was observed on a Sunday, what is the probability that the next risky day will appear on the following Wednesday?

c. Find the probability that the 4th day, which is Thursday, of the week is the second risky day.

Answer IN R CODE to get the following. Using the data below,

1. Create a scatterplot of y vs x
2. Fit a simple linear regression model using y as the response and plot the regression line (with the data)
3. Test whether x is a significant predictor and create a 95% CI around the slope coefficient.
4. Report and interpret the coefficient of determination.
5. For x=20, create a CI for E(Y|X=20).
6. For x=150, can you use the model to estimate E(Y|X=150)? Discuss.
7. Does the model appear to be linear with respect to x? Discuss, and if not, provide alternative model and repeat steps 1-6.

Please provide all relevant work in R code. The commands, the output and any interpretations/conclusions that are necessary.

Answer IN R CODE please. Using the data below,

Create a scatterplot of y vs x (show this) and fit it a simple linear regression model using y as the response and plot the regression line (with the data). Show this as well. Test whether x is a significant predictor and create a 95% CI around the slope coefficient. What does the coefficient of determinations represent?

For x=20, create a CI for E(Y|X=20). Show this.

For x=150, can you use the model to estimate E(Y|X=150). Discuss.

Does the model appear to be linear with respect to x. Explain. Discuss, and if not, provide alternative model and repeat steps 1-6.

Please provide all relevant work in R code. The commands, the output and any interpretations/conclusions that are necessary.

1) Suppose that you have $10,000 to invest and the bank offer you the following options:

A: Interest rate of 8.5% compounded quarterly.

B:Interest rate of 8.3% compounded monthly.

C:Interest rate of 822% compounded weekly.

D: Simple interest rate of 15%

a) Order the options from worst to best, if the term of the investment is 1, 3, 10 and 20 years.

b) What is the minimum number of years required for options A, B and C to be more profitable than option D.

A random sample of 9 recently sold homes in a local market collects the list price and selling price for each house. The prices are listed below in thousands of dollars. A group of realtors wants to test the claim that houses are selling for more than the list price.

(a) Find d¯, the mean of the differences.

(b) State the claim, the negation of the claim, H₀, and H₁ (using equations and the parameter μd).

(c) Find the p-value. Use a significance level of α=.05 to test the claim. State your conclusion about H_0.

(d) State your conclusion about the original claim.