In California, we need more rain to sustain the health of our natural environment, argriculture, and economic. A group of statistics students in Oxnard College recorded the amount of rain during 2016-2017 school year, measuring the intensity by the inches of rain, and the results were:

The mean (¯xx¯) rain intensity: ____ inches (Please show your answer to 1 decimal place.)

The median rain intensity: ____ inches

The mode rain intensity: _____ inches (Please separate your answers by ',' in bimodal situation. Enter DNE if there is no mode.)

In Lesson Ten you’ve worked with techniques for conducting hypothesis tests for two means or two proportions. Work through the following exercise.

Two types of medication for hives are being tested. The manufacturer claims that the new medication B is more effective than the standard medication A and undertakes a comparison to determine if medication B produces relief for a higher proportion of adult patients within a 30-minute time window. 20 out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. 12 out of another random sample of 200 adults given medication B still had hives 30 minutes after taking the medication. The hypothesis test is to be carried out at a 1% level of significance.

State the null and alternative hypotheses in words and in statistical symbols. (3 points)

What statistical test is appropriate to use? Explain the rationale for your answer. (3 points)

Would the test be right-tailed, left-tailed or two-tailed? Explain the rationale for your answer. (3 points)

Describe an outcome that would result in a Type I error. Explain the rationale for your answer. (3 points)

Describe an outcome that would result in a Type II error. Explain the rationale for your answer. (3 points)

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Table

Copy Data

Step 1 of 6 :

Find the estimated slope. Round your answer to three decimal places.

A political committee consists of eight Democrats and five Republicans. A subcommittee of nine people needs to be formed from this group.​ (For this​ problem, define a success as a Democrat being selected for the​ subcommittee.) a. Determine the probability that this subcommittee will consist of five Democrats and four Republicans if they were randomly selected. b. Calculate the mean and standard deviation of this distribution. a. The probability that this subcommittee will consist of five Democrats and four Republicans if they were randomly selected is nothing. ​(Round to four decimal places as​ needed.) b. The mean of this distribution is nothing. ​(Round to three decimal places as​ needed.) The standard deviation of this distribution is nothing. ​(Round to three decimal places as​ needed.)

Please find the range, sample standard deviation and inter-quartile range (IQR) of the following data set using TI-84.

range = _____ (Please enter an exact answer.)
standard deviation (ss) = _______ (Please show your answer to one decimal place.)
Inter-Quartile-Range (IQR) = ________ (Please enter an exact answer.)

A new number, 112, is added to the data set above. Please find the new range, sample standard deviation and IQR of the new data set.

range = ____ (Please enter an exact answer.)
standard deviation (ss) = ______ (Please show your answer to one decimal place.)
IQR = _____ (Please enter an exact answer.)

Which measure of spread is less affected by the addition of the extreme observation?

• IQR
• Range
• standard deviation

A researcher conducts an independent-measures study. One sample of individuals serves as a control group and another sample serves as a treatment group. The researcher hypothesizes that the two samples will be different on the dependent variable.

The data are as follows:

α = .05, two-tailed

a.) Following the steps of a hypothesis test, first determine whether the two groups differ in terms of their sample means.

b.) Second, calculate Cohen’s d and r2.

c.) Finally, Write a sentence demonstrating how the results of the hypothesis test and the measure of effect size (use either d or r2) would appear in a research report.

Construct a 95​% confidence interval to estimate the population mean when x bar =124 and s​ =29 for the sample sizes below.

​a)

n=40     

​b)

n=50       

​c)

n=90

round to 2 decimale places as needed

Construct the confidence interval for the population mean μ. c =0.90​, x=9.8​, σ =0.4​, and n =46

A 90​% confidence interval for μ is ?

Edit question Suppose in an effort to manage his inventory levels better, the owner of two steak and seafood restaurants, both located in the same city, hires a statistician to conduct a statistical study. The owner is interested in whether the restaurant located on the south side sells more halibut fillets per night than the restaurant located on the north side of the city. The statistician selects a random sample of 102 nights that the south-side restaurant is open. The mean number of halibut fillets sold per night at the south-side location is 15.3 with a sample standard deviation of 0.4. Likewise, the mean number of halibut fillets sold per night at the random sample of 83 nights that the north-side restaurant is open is 16.8 with a sample standard deviation of 5.5.

Suppose you intend to conduct a hypothesis test on the difference in population means. In preparation, you identify the sample of nights at the south restaurant as sample 1 and the sample of nights at the north restaurant as sample 2. Organize the provided data by completing the following table:

Sample 1 Sample 2 N1 = N2 = μ1 = μ2 = X‾‾1 = X‾‾2 = σ1 = σ2 = s1 = s2 = The difference in sample means for sample 1 and sample 2 is . The estimate of the standard deviation of the sampling distribution of the differences in sample means, s(X‾‾−X‾‾) , is . Now, you know all that you need to know to answer the question about whether the restaurant located on the south side sells more halibut fillets per night than the restaurant located on the north side of the city.

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, y ˆ = b 0 + b 1 x y^=b0+b1x , for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age 48 48 51 51 56 56 60 60 69 69 Bone Density 351 351 320 320 318 318 311 311 310 310 Table Copy Data Step 2 of 6 : Find the estimated y-intercept. Round your answer to three decimal places.

Discuss the topic most challenging in Inference Regression?

Provide a good description of the mentioned topic

Discuss the reasons for the challenges

Discuss exactly what the challenges are

The following contingency table shows the number of people who took a statistics course classified by type of student and job outcome

                                                                                    Type of student

Job outcome                                                 Undergraduate (B₁)       Graduate (B₂)

Got a job after graduation(A₁)                                    150                             100

Did not get a job after graduation(A₂)                         50                             200

Are the two events in (d) independent? Show mathematically how you arrived at your conclusion.

Let X and Y have the following joint distribution:

Further, suppose σx = √(1664/625), σy = √(3111/2500)

a) Find Cov(X,Y)

b) Find p(X,Y)

c) Find Cov(1-X, 10+Y)

d) p(1-X, 10+Y), Hint: use c and find Var[1-X], Var[10+Y]

3300 Econometics HW Set 1

The data given in the data file in the Consumption file represent the real private consumption of the USA from Quarter I 2005 to III Quarter 2018.

Similarly, the Real Disposable Income is provided over the same time span.

Set up a regression that relates the dependent variable(Y) to the independent variable(X).

Derive Manually the coefficients of the regression. (Intercept(b1) and slope(b2)).

State the Regression equation.

Interpret the meaning of the slopes b2, in this problem.

Derive the Correlation Coefficient R^2

Derive the Standard Error of the regression

Derive the standard error of the Intercept (b1) and the standard error of the Slope (b2).

Derive the t values of the coefficients

Construct a 95% confidence interval for b1 and b2

Use a two tail α=5% level of significance, to test the confidence intervals for the slope(b2).

(Hint: All the formulas required to answer the questions are cited in chapters 2 and 3 of the textbooks. Use also the notes from the lectures).

a) Prove, using the joint density function, and the definition of expectation of a function of two continuous random

variables (i.e., integration) that E (5X + 7Y ) = 5E (X ) + 7E (Y ).

b)

(h) Prove, using the joint density function and the definition of expectation of a function of two continuous random

variables (i.e., integration) that Var (5X + 7Y ) = 25Var (X ) + 49Var (Y ) + 70Cov (X; Y ).