3. A study was conducted to relate birthweight (measured in hundreds of grams) and estriol level (measured in mg/24hr) in 11 pregnant women. A simple linear regression model was fit to the sample data. Use the output from this page to answer the following questions.

   THE REG PROCEEDURE

ANALYSIS OF VARIANCE

   SOURCE DF SUM OF SQUARE MEAN SQUARE F-VALUE PR > F

MODEL 1 228.38    228.381 22.557 0.001045

   ERROR    9    91.12 10.124

TOTAL 10 319.5

   PARAMETER ESTIMATES

   Variable    DF    PARAMETER ESTIMATE STANDARD ERROR    T-VALUE Pr > ltl

   Intercept 1 21.0123 2.4751    8.489 1.5E-05

   estriol    1 0.6306    0.1328    4.749 0.00104

R-square    0.7148   

(a)10 Use the output above to fill in the following blanks to test whether there is a significant linear relationship between estriol level in pregnant women and birthweight:
We are interested in the hypotheses: H0 :___ vs HA :____ ,
where [define any parameters used above] ____
.
We can test this hypothesis using the test statistic ,
which follows a distribution with degrees of freedom if H0 is true.
The p-value for this test is_____ .
So, at a significance level of ↵ =0 .05, we would (circle one):
accept the null hypothesis / reject the null hypothesis / fail to reject the null hypothesis
and conclude that [give your conclusion in the context of the problem of interest and be as specific as possible about the direction and magnitude of any effect]
.

(b)1 Based on above output, what birthweight would you expect for a child born to a mother with an estriol level of 15 mg/24hr?
(c)1 Construct a 95% Confidence Interval for the average birthweight at an estriol level of 15 mg/24hr. (Note that SE(E[Y]) = 0.98).
(d)2 A 95% Prediction Interval corresponding to an estriol level of 15 mg/24hr is (22.92, 38.02). Interpret this interval and contrast it with the interval found in (c).
(e)2 Can estriol be used to explain a large proportion of the variability in birthweight? Justify your answer.
(f)2 Find Pearson’s correlation coefficient for this sample. Interpret this value.
(g)2 Will increasing a mother’s estriol level increase the birthweight of her child? Justify your answer.

(h)4 Explain the assumptions underlying this regression modelling.
(i)4 Use the information from the next page to assess, as much as possible, the suitability of this regression model.
(j)2 Based on all of these considerations, what can you conclude about the relationship between birthweight and estriol level in pregnant women.

A sample of 16 joint specimens of a particular type gave a sample mean proportional limit stress of 8.44 MPa and a sample standard deviation of 0.73 MPa.

(a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)

(b) Calculate and interpret a 95% lower prediction bound for proportional limit stress of a single joint of this type. (Round your answer to two decimal places.)

The contents (in g) of Fritz ketchup bottles are known to follow the Normal distribution with mean 452g and standard deviation 0.5g.

c) Find the percentage of bottles with contents that weigh between 452.5g and 453.5g.

i. Write a probability expression to find the answer: P( ____ )

ii. Complete the sketch of the density curve and shade the appropriate area.

iii. Find the probability.

d) What weight of ketchup content would approximately 16% of the bottles fall below?

i. Write a probability expression to find the answer: P( ____ )

ii. Complete the sketch of the density curve and shade the appropriate area.

iii. Find the weight.

Can I have a reference and intext citation of the software SAS university edition & SAS 9.4 please thank you

In the previous item, we used the Mann-Whitney test rather than an independent t-test. Why might we Mann-Whitney rather than the t-test?

Original question- A sample of nurses with affiliation to private hospitals (affiliation = 0) and to university hospitals (affiliation = 1) was asked to rate their confidence in making the right decisions based on their level of ongoing inservice professional development. Use a Mann-Whitney U-test to determine if the distribution of confidence in each group is the same. Be sure to always write the null and alternate hypotheses, so that the decision is made in the correct direction. Also, conduct all as two-tailed tests at α = 0.05.

Consider the following gasoline sales time series data. Click on the datafile logo to reference the data.

a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent observation, and 1/6 third the most recent observation, compute a three-week weighted moving average for the time series (to 2 decimals). Enter negative values as negative numbers.

b. Compute the MSE for the weighted moving average in part (a).
MSE =

Do you prefer this weighted moving average to the unweighted moving average? Remember that the MSE for the unweighted moving average is 13.69.
Prefer the unweighted moving average here; it has a (greater/smaller) MSE.

c. Suppose you are allowed to choose any weights as long as they sum to 1. Could you always find a set of weights that would make the MSE at least as small for a weighted moving average than for an unweighted moving average?
(Yes/No)

Suppose that the number of requests for assistance received by a towing service is a Poisson process with rate α = 6 per hour.

a) Find expected value and variance of the number of requests in 30-minutes. Then compute the probability that there is at most one request in 30-minute interval. Clearly state the random variable of interest using the context of the problem and what probability distribution it follows.

b) What is the probability that more than 20 minutes elapse between two successive requests? Clearly state the random variable of interest using the context of the problem and what probability distribution it follows.

QUESTION 4: The returns for an asset are normally distributed. The mean return is 9.75% and the standard deviation is 3.25%. a. What is the probability of earning a negative return? (3 points) b. What is the probability of earning a return between 6.5% and 16.25%? (3 points) c What is the probability of earning a return greater than 13%? (3 points)

Randall grew up in Ohio but now lives in California. He knows that snow sucks and makes driving a nightmare. His father, Douglas, owns a specialty cars dealership chain in Ohio. Douglas knows that it is very hard to sell sports cars in the winter. So, they see a business opportunity where they can ship and sell Corvettes from Ohio to California in the winter. They can make a profit of $3,000 per car sold. This year Doug has 57 Corvettes in his Columbus store, 55 in Cincinnati store, and 20 in his Cleveland store. Randall is able to broker deals with California dealers: VetteMax will buy 25, BlingRide is committed to 30, Americana signs a contract for 20, and BoyToys will buy 45.

The associated shipping costs are as follows:

a. How many Corvettes does BoyToys get from Columbus?

b.What is the total shipping cost?

c.What is their NET profit?

What is a residual plot and how should it look?

What kind of statistical test would you use?

What is Cook's distance?

What are “LINE” approximations in regression analysis?

Question 1

For correlation, you will ask if the slope of the line relating variable X and variable Y is significantly different from zero

1. True
2. False

Question 2

For regression, you test if the R2 value is significantly different from zero

1. True
2. False

Question 3

For correlation, the data are assumed to be normally distributed in both the X and the Y directions.

1. True
2. False

Question 4

For regression, the data are assumed to be normally distributed in both the X and Y directions.

1. True
2. False

Question 5

For correlation, the alternative hypothesis can be left, right or both tailed depending on the question

1. True
2. False

Question 6

For regression, the alternative hypothesis can be left, right or both tailed depending on the question

1. True
2. False

Question 7

Nonparametric tests use the original data to analyze the question being asked

1. True
2. False

Question 8

In class we covered a nonparametric tests for every parametric test covered this semester

1. True
2. False

Question 9

Nonparametric tests still have the assumptions of a 'good' sample

1. True
2. False

Question 10

For the Spearman's Rank Test, there still has to be a pattern of covariance in ranks to find a significant relationship between your X and Y variables.

1. True
2. False

An electric company received a shipment of several thousand resistors with 100 ohm ratings. A sample of nine resistors was measured with a laboratory standard instrument and gave the following measurements (assume that the population distribution of the measurements is normal): 102.0 103.9 101.4 103.7 102.6 102.2 104.2 101.9 100.6 a. Get the 95% confidence interval for the mean rating in ohms of this shipment of resistors. b. Get the 95% confidence interval for the variance of the ratings in ohms of this shipment of resistors. c. Get the 95% confidence interval for the standard deviation of the ratings in ohms of this shipment of resistors.

QUESTION 4

1. A researcher is interested in testing whether there is a difference in aggression levels between kids who watch only TV shows, only play video game, or watch TV and play video games. Which statistical test should be used to determine whether a difference exists in aggression levels for these 3 groups?

   		T-Test for One Sample
   		T-Test for Independent Samples
   		T-Test for Related Samples
   		One-Way ANOVA
   		Two-Variable Chi Square Test

Question 5:

A psychologist is interested in the relationship between people born during three different decades (<80’s, 90’s, 00’s) and their liking for Social Media. The psychologist studies 200 adults in Boston. The results are shown in the table below.

Compute this statistic using a .05 level of significance

In your response, state the Research Question, Critical Value, Calculations, and state whether you retain/reject the null hypothesis

In a study of monthly salary distribution of residents in Paris conducted in year 2015, it was found that the salaries had an average of €2200 (EURO) and a standard deviation of €550. Assume that the salaries were normally distributed.

Question 1: Consider sampling with sample size 64 on the above population. Compute the mean of the sampling distribution of the mean (?̅).

Question 2: Compute the standard deviation of the sampling distribution of the mean in Question 1 above.

Question 3: A random sample of 64 salaries (sample 1) was selected from the above population. What is the probability that the average of the selected salaries is above €2330?

Question 4: Would the calculation you performed in Question 3 still be valid if the monthly salaries were NOT normally distributed? Why? In another study conducted in the same year (2015), the average monthly salary of residents in Bordeaux was found to be about €2353. And the standard deviation of the monthly salaries was €420. A random sample of 81 salaries (sample 2) was selected from this population. Set 1 = Paris (2015); 2 = Bordeaux (2015)

Question 5: Compute the mean of ?̅ 1 − ?̅ 2.

Question 6: Compute the standard deviation of ?̅ 1 − ?̅ 2.

Question 7: What is the probability that the average of the salaries in the sample 1 is less than the average of the salaries in sample 2? In 2017, a study on the salary distribution of Paris residents was conducted. Assume that the salaries were normally distributed. A random sample of 10 salaries was selected and the data are listed below: 3200 3500 3000 2100 2950 2050 2440 3100 3500 2500

Question 8: Assume that the standard deviation of the salaries was still the same as in 2015. Estimate the average salary (in 2017) with 95% confidence.

Question 9: The assumption made in Question 8 was certainly unrealistic. Estimate the average salary (in 2017) with 95% confidence again assuming that the standard deviation had changed from 2015.

Question 10: Estimate the variance of monthly salaries of Paris residents (in 2017) based on the sample provided above at a 95% confidence level.

Question 11: How would you interpret the result in Question 10 above? A similar study was conducted on salary distribution of Paris residents in 2019. The research team aimed to estimate the average salary. They chose the 98% confidence and assumed that the population standard deviation was the same as in 2015. Assume again that those salaries were normally distributed.

Question 12: If they would like the (margin of) error to be no more than €60, how large a sample would they need to select?