1.) Using excel. A random number generator picks a number from one to nine in a uniform manner.

1. X ~ _________
2. Graph the probability distribution.
3. f(x) = _________
4. μ = _________
5. σ = _________
6. P(3.5 < x < 7.25) = _________
7. P(x > 5.67)
8. P(x > 5|x > 3) = _________
9. Find the 90^th percentile.

2) using excel A subway train on the Red Line arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution.

1. Define the random variable. X = _______
2. X ~ _______
3. f(x) = _______
4. μ = _______
5. σ = _______
6. Find the probability that the commuter waits less than one minute.
7. Find the probability that the commuter waits between three and four minutes.

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 76 cars owned by students had an average age of 8.72 years. A sample of 119 cars owned by faculty had an average age of 8.95 years. Assume that the population standard deviation for cars owned by students is 3.64 years, while the population standard deviation for cars owned by faculty is 3.51 years. Determine the 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 1 of 3 : Find the point estimate for the true difference between the population means

Suppose an object is 4 sided marked as {1,2,3,.., 4. Now you toss this object 4 times. Let nS be the number of outcomes in this sample space. Let A be the event consisting of all outcomes in which 2 occurs at least once. How many outcomes are there in A? It is whole number. Computer follows comma rule when entering large numbers. For example, 1123 is entered as 1,123

A lead inspector at ElectroTech, an electronics assembly shop, wants to convince management that it takes longer, on a per-component basis, to inspect large devices with many components than it does to inspect small devices because it is difficult to keep track of which components have already been inspected. To prove her point, she has collected data on the inspection time (Time in seconds) and the number of components per device (Components) from the last 25 devices. A portion of the data is shown in the accompanying table.

a-1. Estimate the linear, quadratic, and cubic regression models with Time as the response variable. Report the Adjusted R² for each model. (Round answers to 4 decimal places.)

a-2. Based on adjusted-R² only, which model has the best fit?

• Cubic model

• Linear model

• Quadratic model

b. Use the best model to predict the time required to inspect a device with 38 components. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

A certain flight arrives on time 82 percent of the time. Suppose 193 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that

​(a) exactly 159 flights are on time.

​(b) at least 159 flights are on time.

​(c) fewer than 152 flights are on time.

​(d) between 152 and 173​, inclusive are on time.

If the critical t-value for a confidence interval calculation was 2.756, how big
was the sample?

A tax preparation firm claims that the average savings from their tax review is more than $2,500. if we wish to evaluate this claim through hypothesis testing the proper hypothesis statement is

Ho: u (=, >, <, >=, <=, not=) 2500

H1: u (=, >, <, >=, <=, not=) 2500

A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. SUVs equipped with tires using compound 1 have a mean braking distance of 56 feet and a standard deviation of 6.4 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 58 feet and a standard deviation of 6.6 feet. Suppose that a sample of 80 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ1 be the true mean braking distance corresponding to compound 1 and μ2 be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance.

Step 1 of 4:

State the null and alternative hypotheses for the test.

Step 2 of 4:

Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4:

Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to three decimal places.

Step 4 of 4:

Make the decision for the hypothesis test.

1. A new low fat/carbohydrate diet was designed to assist with weight loss. From a population of obese people, 100 are randomly selected to go on the new diet, while another 100 are selected to eat a diet of a similar quantity of food but not as low in fats and carbohydrates. The weight loss of each of the 200 people are in the Excel file "Extra HW 1 Diet Study". Use 0.05 significance and answer the following.

   1. Whataretheappropriatehypothesestotestwhetherthereisevidenceforadifferencein mean weight loss between people who eat these diets?

   2. Findtheappropriatet-scoreandP-value.

   3. StatetheconclusionofthetestinanEnglishsentence.

      Lowfat	Regular
      8	6
      10	6
      10	5
      12	5
      9	2
      3	6
      11	10
      7	3
      9	9
      2	11
      21	14
      8	4
      9	10
      2	13
      2	3
      20	8
      14	8
      11	13
      15	9
      6	3
      13	4
      8	12
      10	6
      12	11
      1	12
      7	9
      10	8
      13	5
      14	8
      4	7
      8	6
      12	2
      8	6
      10	8
      11	5
      19	7
      0	16
      9	18
      10	6
      4	8
      11	13
      7	1
      14	9
      12	8
      11	12
      12	10
      4	6
      12	1
      9	0
      2	13
      4	11
      3	2
      3	8
      5	16
      9	14
      9	4
      4	6
      3	5
      5	12
      12	9
      3	11
      12	6
      7	3
      13	9
      11	9
      11	14
      13	2
      12	10
      18	4
      9	13
      6	8
      14	1
      14	1
      18	4
      10	9
      11	4
      7	1
      9	1
      7	5
      2	6
      16	14
      16	0
      11	7
      11	12
      3	9
      15	5
      9	9
      5	12
      2	7
      6	9
      5	8
      11	9
      14	8
      11	10
      6	5
      9	8
      4	0
      17	3
      20	4
      10	8

A sample of 30 randomly selected student cars have ages with a mean of 7.3 years and a standard deviation of 3.6 years, while a sample of 19 randomly selected faculty cars have ages with a mean of 5 years and a standard deviation of 3.7 years.

1. Use a 0.01 significance level to test the claim that student cars are older than faculty cars.

(a) The test statistic is ???

(b) The critical value is ???

(c) Is there sufficient evidence to support the claim that student cars are older than faculty cars?

A. No

B. Yes

2. Construct a 99% confidence interval estimate of the difference μs−μf, where μs is the mean age of student cars and μf is the mean age of faculty cars.

???<(μs−μf)<???

Suppose we are interested in modeling the factors that affect salaries of CEO’s of companies. Let salaryi denote CEO compensation in 1990 measured in $1000 increments. Let salesi denote the 1990 sales of a firm in millions of dollars. Let mktvali denote the market value of the firm at the end of 1990 in millions of dollars. Let profitsi denote 1990 profits in millions of dollars. Finally, let the dummy variable collegei = 1 if a CEO attended college and 0 otherwise and let the dummy variable gradi = 1 ,if a CEO attended graduate school and 0 otherwise.
First consider a simpler model where log denotes the natural logarithm (log base e):
log(salaryi) = β1 + β2 log(salesi) + β3 log(mktvali) + εi.
Assume that Classical Assumptions for MLR hold. This regression was estimated using a random sample of 177 firms. Standard errors are in parentheses:
log(sal?aryi) = 4.62 (0.25)
R2 = 0.299
(a) Test the joint significance of β2 and β3 at the 1% significance level.
Suppose an undergraduate RA student majoring in economics was working on this empirical question. Given the lack of training, this student could only think to estimate the simple regression model
log(salaryi) = β1 + β2 log(salesi) + εi. and he only reported that RSS from this regression was 46.51.
(b) Would the R2 from this simple regression be larger or smaller than 0.299? Give an explanation for your answer.
One might think that the profits of a firm would affect CEO pay (the more a firm makes, the more it can pay its CEO). Consider the following fitted model
log(sal?aryi) = 4.69 +0.161 log(salesi) +0.098 log(mktvali) +0.000036profitsi
(0.38) (0.04)
(0.064) (0.00015)
+0.162 log(salesi) +0.170 log(mktvali) (0.04) (0.05)
RSS = 45.31 TSS = 64.65 RSS = 43.295
(c) Test for the joint significance of the two slope parameters for log(mktval) and profits at the 1% signif-
icance level.
A more complete model of CEO salaries would take into effect the education of the CEOs:
log(salaryi) = β1 + β2 log(salesi) + β3 log(mktvali) + β4collegei + β5gradi + εi. (1)
This model was estimated by OLS yielding
log(sal?aryi) = 4.68 +0.160 log(salesi) +0.112 log(mktvali) −0.056collegei −0.057gradi
(0.35) (0.04)
(0.05) (0.237) (0.080)
RSS = 43.137

For this lab we will use NFL Scouting Combine data for drafted running backs and wide receivers from years 2012-2014.The combine is a series of tests to evaluate college football players ahead of the NFL Draft. The dataset is available on Canvas. To perform the hypothesis tests below, you will need to upload the data to StatKey and select the appropriate columns. For guidance, refer to the StatKey guide.The dataset contains the following variables:

year Year player participated in combine

position Running Back (RB) or Wide Receiver (WR)

height height in inches

weight weight in pounds

forty yd forty yard dash time in seconds

three cone three cone time in seconds (run between 3 cones in an L shape)

vertical vertical jump height in inches

broad broad jump distance in inches

bench number of bench press repetitions with 225lbs

round round player was drafted (1-7)

Activity 1: Strength and Draft RoundIs there a linear association between a player’s strength, measured using the bench variable,and the round he was drafted in?

1.State the hypotheses of interest.

2.What is the notation and value of the sample statistic?

3.Use StatKey to generate a randomization distribution for these hypotheses. Remember, you will have to upload the dataset to StatKey and select the correct variables.What is the p-value?

4.Complete the p-value interpretation below:If there is ______ linear association between the round he was drafted in and a player’s strength in the population, the chance of seeing a sample correlation of _______ or ___________is _______________.

5.What is the formal conclusion at a significance level of 0.05?

6.What is the conclusion in context?

1. You are involved in a study of the relationship between smoking and serum cholesterol concentrations of high-density lipoprotein cholesterol (HDL-C), the following data were collected from samples of adult males who were nonsmokers, light smokers, moderate smokers, and heavy smokers. You wish to know if these data provide sufficient evidence to indicate that the four populations differ with respect to mean serum concentration of HDL-C. Let the probability of committing a type I error be 0.05. If an overall significant difference is found, determine which pairs of individual sample means are significant different.

A scientist claims that pneumonia causes weight loss in mice. The table shows the weights​ (in grams) of six mice before infection and two days after infection. At

alphaαequals=0.050.05​,

is there enough evidence to support the​ scientist's claim? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (e) below.