Ten randomly selected people took an IQ test A, and next day they took a very similar IQ test B. Their scores are shown in the table below.

1. Consider (Test A - Test B). Use a 0.050.05 significance level to test the claim that people do better on the second test than they do on the first. (Note: You may wish to use software.)

a) What is the test statistic?

b) What is the critical value?

c) Construct a 9595% confidence interval for the mean of the differences. Again, use (Test A - Test B).

2. Measuring the height of a California redwood tree is very difficult because these trees grow to heights of over 300 feet. People familiar with these trees understand that the height of the tree is related to other characteristics of the tree, such as the diameter of the tree at the breast height of a person. In the Excel data file for this assignment, under the tab Redwood, is a random sample of 21 redwood trees including the height (in feet) and the diameter (in inches) at breast height.

a. Create the appropriate scatter plot and calculate the coefficient of correlation. Comment on the results. Does it appear a linear relationship exists?

b. Use the least-squares method to compute the regression coefficients b₀ and b₁.

c. Interpret the meaning of b₀ and b₁ in this problem.

d. What if the predicted mean height for a tree that has a breast height diameter of 25 inches? 60 inches?  

e. Determine the coefficient of determination, R², and explain its meaning in this problem.  

g. Perform a complete residual analysis. Does the analysis support all the assumptions required for a valid model? Explain.

h. Create the 95% confidence interval and the 95% prediction interval for a tree with a diameter of 25”. Interpret your results.

i. What conclusions can you reach about the relationship between the diameter of the tree and its height?

You are the manager of a beer distribution center and you want to determine a method for allocating beer delivery costs to the customers. Although one cost clearly relates to travel time within a particular route, another variable cost reflects the time required to unload the cases of beer at the delivery point. You want to develop a model to predict this cost, so you collect a random sample of 20 deliveries within your territory. The unloading time and the number of cases are shown in the Excel data file for this assignment, under the tab Delivery.

i. Construct a 95% confidence interval estimate of the mean time to unload 150 cases of beer and a 95% prediction interval of the unloading time for a single delivery of 150 cases of beer. Explain your results.

j. What conclusions can you reach from the analysis above regarding the relationship between unloading time and the number of cases of beer delivered?

k. If your delivery cost is $100 per hour, what variable cost for unloading 150 cases of beer should you add to that customers invoice?   Explain your thought process.

Researchers were interested in the relationship between the type of prison the inmate is attending (High, Medium, Minimum) and the prison history of their parents (Both, None, One).  Below is the two-way table of the observed data.

What proportion of inmates with both parents in prison are in high security prisons?

If there was no relationship between the type of prison and the prison history of their parents, what proportion of inmates with both parents in prison would be in high security prisons?

The researchers are interested in testing the relationship between prison history of the parents and the type of prison an inmate is attending. What are the appropriate null and alternative hypotheses to test this relationship?

What are the degrees of freedom for the Chi Square test?

What are the missing expected counts under the null hypothesis?

If the P-value is greater than 0.25, is there evidence of a relationship between the prison history of the parents and the type of prison an inmate is attending?

Assuming that the world population continue to grow at its current rate, how many years would it take for the world population to grow.

Hint: rate of natural increase: 0.012 is the value of "r" that you will use in the calculations below.

Remember, net migration is 0 at the global level, so the rate of natural increase (RNI) is the growth rate(r) for the world population.

Second, what is the size of the world population in 2018, according to the world population datasheet?

P₂₀₁₈ = 7,621,000,000

Now, Use the Exponential Grown Rate formula and solve for n.

A.) How long would it take to grow by 50%

B.) How long would it take to Quadruple?

C.) How long would it take to add the next 1 billion?

(1 point) In a sample of 40 grown-ups, the mean assembly time for a boxed swing set was 1.86 hours with a standard deviation of 0.46602 hours. The makers of this swing set claim the average assembly time is less than 2 hours.

(a) Find the test statistic.

(b) Test their claim at the 0.01 significance level.

Critical value:

Is there sufficient data to support their claim?
Yes
No

(c) Test their claim at the 0.05 significance level.

Critical value:

Is there sufficient data to support their claim?
Yes
No

(1 point) Ben thinks that people living in a rural environment have a healthier lifestyle than other people. He believes the average lifespan in the USA is 77 years. A random sample of 20 obituaries from newspapers from rural towns in Idaho give ?¯=78.81 and ?=1.86

. Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years?

(a) State the null and alternative hypotheses: (Type "mu" for the symbol ?

, e.g. mu >1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1)
?0 :
??

:

(b) Find the test statistic, t =

(c) Answer the question: Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years? (Use a 10% level of significance)
(Type: Yes or No)

(1 point) The hypothesis test

?0:?=36?1:?≠36

is to be carried out. A random sample is selected, and yields ?¯=38 and s = 15. If the value of the t statistic is ?=0.692820323027551

, what is the sample size? (If rounding is required, round to the nearest integer.)

Sample Size =

(1 point) Our decisions depend on how the options are presented to us. Here's an experiment that illustrates this phenomenon. Tell 20 subjects that they have been given $50 but can't keep it all. Then present them with a long series of choices between bets they can make with the $50. Scattered among these choices in random order are 64 choices between a fixed amount and an all-or-nothing gamble. The odds for the gamble are always the same, but 32 of the fixed options read "Keep $20" and the other 32 read "Lose $30." These two options are exactly the same except for their wording, but people are more likely to gamble if the fixed option says they lose money. Here are the percent differences ("Lose $30" minus "Keep $20") in the numbers of trials on which the 20 subjects chose to gamble:

If we make a stemplot, we would find the stemplot shows a slight skew to the right, but not so strong that it would invalidate the t procedures. All 20 subjects gambled more often when faced with a sure loss than when faced with a sure win. Give a 90% confidence interval for the mean percent increase in gambling when faced with a sure loss.

Describe a way that statistical control charting could be applied to a human task in the social sciences, education, health care, or business to monitor and improve performance.

An inexpensive restaurant featuring steak dinners makes most of its profit from side orders suggested to diners by the staff. As an experiment, the restaurant owner rewarded each server with 10% of the price of all side orders made through the server. After 10 days, the owner computed the side-order volume per customer for each of 41 servers. The data are in column 1 of the Excel data file named ‘Side Orders’. The reward policy will be profitable if the mean volume is more than $2.40 per customer. At the 10% level of significance, is there a strong evidence in the data that the policy will, in fact be profitable? Please show the necessary steps and explain your conclusion.       

1. Calculate the expected values of the null hypothesis, and put these into a table.  

2. Calculate the Chi-Squared value for the observed data.

3. Calculate the degree of freedom.

4. Find the critical value using the Chi-Square critical value

A random sample of 81 items is selected from a population of size 350. What is the probability that the sample mean will exceed 205 if the population mean is 200 and the population standard deviation equals 25​? ​(Hint: Use the finite population correction factor since the sample size is more than​ 5% of the population​ size.)

The time spent​ (in days) waiting for a heart transplant for people ages​ 35-49 can be approximiated by the normal​ distribution, as shown in the figure to the right. ​(a) What waiting time represents the 55th ​percentile? ​(b) What waiting time represents the third​ quartile?

Mean= 203

Standard Deviation= 23.1

Round to the nearest integer as needed

A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that a recent sample of 1,000 adults showed 460 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 850 adults showed 340 indicating that their financial security was more than fair.

(a) State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.

(b) Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion?

(c) What is the 95% confidence interval estimate of the difference between the two population proportions? What is your conclusion?

Consider a statistical expirement of flipping a pair of fair coins simultaneously. Let X & Y be the number heads in flipping each coin.

Define a joint density function Z = XY. (I provided the answers in bold but I need help understanding how it is solved. Thank you in advance).

a) The number of possible distinct values of Z is: 2

b) The probability of Z = 0 is: 3/4

c) The mean of Z is: 1/4

d) The standard deviation of Z is: sqrt(3/16)

e) The correlation coefficient of X and Y is: 0

f) Which RV follows a uniform distribution among all three random variables, X, Y, and Z? X & Y

1. Some data gathered by the Department of Education which relates education levels based on

scores: achievement tests given to high school students for example

urban: factor. Is the school located in an urban area?

distance: distance from a 4-year college (in 10 miles)

tuition: average state 4year college tuition (in 1000 USD).

        Coefficients:

               Estimate Std. Error t value Pr(>|t|)    

        (Intercept)  9.141015   0.148905  61.388  < 2e-16 ***

        score        0.095596   0.002679  35.686  < 2e-16 ***

        urbanyes     0.025619   0.057090   0.449   0.6536    

        distance    -0.048723   0.010539  -4.623 3.88e-06 ***

        tuition     -0.142627   0.068517  -2.082   0.0374 *  

        ---

        Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

        Residual standard error: 1.58 on 4734 degrees of freedom

        Multiple R-squared:  0.221,   Adjusted R-squared:  0.2203 

        F-statistic: 335.7 on 4 and 4734 DF, p-value: < 2.2e-16

1. What is the estimated regression equation?
2. What variables are significant?
3. How do you interpret the variable urban (yes/no)?
4. How much of the variance in the model can be explained by the variables that you included?
5. In general what information does VIF regression give you in assessing a model?
6. An output from R shown below, gives the Variance Inflation Factors for your model. What do these numbers tell you?

        score     urban     distance  tuition 

        1.031628  1.105871  1.112577  1.027281