Let X1,...,Xn be i.i.d. N(θ,1), where θ ∈ R is the unknown parameter.

(a) Find an unbiased estimator of θ^2 based on (Xn)^2.

(b) Calculate it’s variance and compare it with the Cram ́er-Rao lower bound.

• Bud Light ran a SuperBowl advertisement stating that it does not use corn syrup – in direct contrast to its competitors. The Bud Light marketing department wants to know the impact of the ad (IV) on consumer brand perceptions (DV). They therefore compare consumer perceptions of the brand collected before the SuperBowl with consumer perceptions of the brand collected after the ad was shown in the SuperBowl.
  • What form of study design is this?
  • Will the researcher be able to make claims about causality with this study?

• Les wants to know whether a funny ad or a serious ad is more effective at getting consumers to like his company, XYZ Toys. He randomly assigns 100 consumers to watch the funny ad, the serious ad, or no ad at all (IV). After they watch the ad, he asks them how much they like XYZ Toys on a scale from 1 (Dislike a great deal) to 7 (Like a great deal) (DV).
  • What form of study design is this?
  • Will the researcher be able to make claims about causality with this study?

Tire Kingdom installs automobile tires on a first-come-first-served basis. A random sample of 40 customers experienced an average wait time of 90.5 minutes. Assume that the standard deviation of the total wait time for all customers is 20.6 minutes. Determine the 90% confidence interval for this sample.

A typical California license plate consists of a 7-character string as in the image below. The string startswith a number, is then followed by three letters from the alphabet, and then followed by three more numbers.Count the number of possible different license plates that can be formed in this fashion. How many different license plates have the same exact letter permutations (e.g. ‘7XHL245’ and ‘3XHL901’ have the same letters,? How many different license plates are there that contain a vowel for the firstletter and have an odd number in the last slot and the first slot does not contain a 6?

The fill amount of bottles of a soft drink is normally​ distributed, with a mean of 1.0 liter and a standard deviation of 0.06 liter. Suppose you select a random sample of 25

bottles.

a. What is the probability that the sample mean will be between 0.99 and1.0 liter​?

b. What is the probability that the sample mean will be below 0.98 liter?

c. What is the probability that the sample mean will be greater than 1.01 ​liters?

d. The probability is 90​% that the sample mean amount of soft drink will be at least how​ much?

e. The probability is 90​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)

Suppose that Xi’s are coming from a normal population with a mean μ =10 and known variance σ=2. Generate 100 samples of n=50 observations coming from the population of interest. Please, construct the 90% confidence interval for each sample and report the number of confidence intervals that include the mean μ  value. Compare this number with the expected number of confidence intervals that include the mean μ value.

please help me. i colud not solve it

A study of randomly selected Americans found that of 1,792 men, 244 had cardiovascular disease (CVD) and of 2,007 women, CVD was prevalent in 135 of them. Conduct a hypothesis test to see if CVD prevalence is higher among men than women in America. Let men be group 1 and women be group 2.

A. Write the hypotheses for this test.

B. What is the test statistic?

C. What is the p-value?

D. Using α = 0.05, decide whether or not to reject the null hypothesis.

E. Based on your decision, is there evidence that CVD prevalence is higher among men than women in America?

Please find or gather Statistical data and provide a real-life example of Continuous Random Variables with full steps. you may try to conduct your own experiment/survey/data collection for occurrences of events you come across your daily life. the Creativity of the idea will be rewarded for the assignment. you may also use data set from the internet. please solve with full steps and find all thing in Continuous Random Variables such as probability density function, and the expected value in your example is and please provide a table for you answers at the end.

thanks

Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). The MegaStat output is reported below.

1. Write out the regression equation. (Round your answers to 3 decimal places.)

2. a-2. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage?

3. How much damage would you estimate for a fire 6 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)

4. c-1. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

5. c-2. Fill in the blank below. (Round your answer to one decimal place.)

6. d-1. Determine the correlation coefficient. (Round your answer to 3 decimal places.)

7. d-2. Choose the right option.

8. d-3. How did you determine the sign of the correlation coefficient?

9. e-1. State the decision rule for 0.01 significance level: H₀ : ρ = 0; H₁ : ρ ≠ 0. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)

10. e-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

11. e-3. Is there any significant relationship between the distance from the fire station and the amount of damage? Use the 0.01 significance level.

The data in the worksheet labeled “Problem 5&6” in the file “Test 3 Data” provides samples of size 8, collected each hour, for a particular process.

a. Construct an X-bar chart for this process.

b. Does the process appear to be in control? Why or why not?

An office supply company services copiers and tracks how many machines are serviced and the length of time (in minutes) for a service call. The data below for 11 clients is below.

Sum X = 46 Sum Y= 234 Sum XY = 5797 Sum X² =1180 Sum Y² =146608

1) Calculate SS_YY, SS_XX, SS_XY

2) Calculate b₀, b₁

3) Interpret the estimated slope coefficient.

4) Construct the appropriate ANOVA table.

5) Calculate R².

6) Interpret the coefficient of determination.

6) Calculate r.

7) Calculate the calculated t statistic for testing the slope coefficient.

8) Calculate the calculated t statistic for testing the correlation coefficient.

9) Find the residuals for observations #2 (X = 4 ; Y = 109) and #4 (X = 7; Y = 189)

Suppose the following data were collected relating CEO salary to years of experience and gender. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average male CEOs have higher salaries than female CEOs at the 0.050.05 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."

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SALARYi=SALARYi= b0  ++ b1 EXPERIENCEiEXPERIENCEi ++ b2 MALEi+eiMALEi+ei  There is not enough evidence

The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .28.

a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)? Use 95% confidence.

b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?

c. What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)?