What direction of bias would weaken a conclusion that there was no
association between exposure and outcome?
Choose the single best answer: “toward the null”, “away from the null”, or
“cannot determine from the given information”.

Consider the hypotheses shown below. Given that x overbarequals57​, sigmaequals13​, nequals35​, alphaequals0.10​, complete parts a and b. Upper H 0​: muless than or equals54 Upper H 1​: mugreater than54

A consumer preference study compares the effects of three different bottle designs (A, B, and C) on sales of a popular fabric softener. A completely randomized design is employed. Specifically, 15 supermarkets of equal sales potential are selected, and 5 of these supermarkets are randomly assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is recorded. The data obtained are displayed in the following table.

The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below.

  Click here for the Excel Data File

(a) Test the null hypothesis that μ_A, μ_B, and μ_C are equal by setting α = .05. Based on this test, can we conclude that bottle designs A, B, and C have different effects on mean daily sales? (Round your answer to 2 decimal places.)

(b) Consider the pairwise differences μ_B – μ_A, μ_C – μ_A , and μ_C – μ_B. Find a point estimate of and a Tukey simultaneous 95 percent confidence interval for each pairwise difference. Interpret the results in practical terms. Which bottle design maximizes mean daily sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

(c) Find a 95 percent confidence interval for each of the treatment means μ_A, μ_B, and μ_C. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Suppose X follows a Gamma distribution with parameters α, β, and the following density function f(x)= [x^(α−1)e^(−x/ β)]/ Γ(α)β^α . Find α and β so that E(X)= Var(X)=1. Also find the median for the random variable, X.

1. Pick three bills from the last 12 months and change the values into z-scores. What does the z-score tell you about that particular month?
2. Between what two values would be considered a normal bill? Remember, being within 2 Standard Deviations is considered normal.

A random sample of

10191019

adults in a certain large country was asked​ "Do you pretty much think televisions are a necessity or a luxury you could do​ without?" Of the

10191019

adults​ surveyed,

522522

indicated that televisions are a luxury they could do without. Complete parts​ (a) through​ (e) below.Click here to view the standard normal distribution table (page 1).

LOADING...

Click here to view the standard normal distribution table (page 2).

LOADING...

​(a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.

ModifyingAbove p with caretpequals=nothing

​(Round to three decimal places as​ needed.)

​(b) Verify that the requirements for constructing a confidence interval about p are satisfied.

The sample

▼

is stated to be

can be assumed to be

cannot be assumed to be

is stated to not be

a simple random​ sample, the value of

▼

n ModifyingAbove p with caretnp

n ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesisnp1−p

ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesisp1−p

nn

ModifyingAbove p with caretp

is

nothing​,

which is

▼

greater than or equal to

less than

​10, and the

▼

sample size

population proportion

sample proportion

population size

▼

is stated to not be

cannot be assumed to be

can be assumed to be

is stated to be

less than or equal to​ 5% of the

▼

sample size.

population size.

sample proportion.

population proportion.

​(Round to three decimal places as​ needed.)

​(c) Construct and interpret a

9595​%

confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without. Select the correct choice below and fill in any answer boxes within your choice.

​(Type integers or decimals rounded to three decimal places as needed. Use ascending​ order.)

A.We are

nothing​%

confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between

nothing

and

nothing.

B.There is a

nothing​%

chance the proportion of adults in the country who believe that televisions are a luxury they could do without is between

nothing

and

nothing.

​(d) Is it possible that a supermajority​ (more than​ 60%) of adults in the country believe that television is a luxury they could do​ without? Is it​ likely?

It is

▼

possible, but not likely

not possible

likely

that a supermajority of adults in the country believe that television is a luxury they could do without because the

9595​%

confidence interval

▼

does not contain

contains

nothing.

​(Type an integer or a decimal. Do not​ round.)

​(e) Use the results of part​ (c) to construct a

9595​%

confidence interval for the population proportion of adults in the country who believe that televisions are a necessity.The

9595​%

confidence interval is

​(nothing​,nothing​).

​(Round to three decimal places as​ needed.)

Click to select your answer(s).

Please answer all

A telescope contains 3 large mirrors. The time (in years) until a single mirror fails has been investigated by your colleagues. You now know that the probability that a mirror is still fully functional after t years is

R(t) = exp −(t/9.4)6

1. (a) All mirrors must be working to take the most detailed photographs. What is the proba-

   bility that the telescope can produce these types of pictures for at least 6 years?

2. (b) The lowest resolution photographs can be taken as long as at least one mirror is work- ing. What is the probability that these photographs can be taken for at least 5 years?

3. (c) The most common photographs the telescope will be taking are of medium resolution. This is possible as long as at least two mirrors are working. What is the probability that this remains possible for at least 7 years?

How do you interpret the coefficient of determination, coefficient of alienation, standard error of estimate

How do you Interpret the meaning of the different coefficients (b0, b1, b2, b3,b4,…bn) in a multiple regression? (slightly different from the interpretation in simple regression)

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those​ tests, with the measurements given in hic​ (standard head injury condition​ units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified​ requirement? 669 635 1144 661 600 749

Questions 1 through 12 are based on the following You work for a men’s designer apparel company based in the US that is planning to expand to the Netherlands. Your target market is young professional men in the age range 24-35. You conducted a survey of 239 Dutch people that satisfies this criterion. From this survey, you have the following information: average income = $43,348.44, standard deviation = $21,989.02, Standard Error = $1422.35

Question 1

The above income information obtained from the survey pertains to

a.The population of Dutch professional men in the age range 24-35

b. The sample of 239 Dutch professional men in the age range 24-35

c. Sampling distributions of the average income (n=239) of Dutch professional men in the age range 24-35

Question 2

The mean of the sampling distribution (n=239) of the average income of Dutch professional men in the age range 24-35 is

a. $43,348.44

b.$45,905.00

c.We need a confidence interval estimate

Question 3 The standard deviation of the sampling distribution of the average income (n=239) of Dutch professional men in the age range 24-35 is

a. $21,989.02

b.$1422.35

c.We need to calculate the z-value

Question 4

You would like to know if the average income of your target market in the Netherlands is different from the US market. In the US, the average income is $45,000. In the past, your company did not expand to another country if the average income of the target market was different from the US. What are the appropriate null and alternative hypotheses to pursue your research question? Group of answer choices

a.Null Hypothesis: The average income of Dutch professional men in the survey is $45,000; Alternative Hypothesis: The average income of Dutch professional men in the survey is different from $45,000

b.Null Hypothesis: The average income of Dutch professional men aged 24 - 35 is $45,000; Alternative Hypothesis: The average income of Dutch professional men aged 24 - 35 is different from $45,000

c.None of the above

Question 5

From the above sample, the 90% confidence interval estimate of the average income of Dutch target market is [$40,999.74, $45,697.15]. Based on this information,

a.Reject the Null Hypothesis at 10% level of significance

b.Fail to Reject the Null Hypothesis at 10% level of significance

c.We need more information

Question 6

What is the Z-value (Ztest) of the hypothesis test? ______ (round up to 2 decimal points).

Question 7

At 10% level of significance, the rejection region to test your hypothesis is:  

a.Z < -1.16 or Z >1.16

b.Z < - 1.96 or Z > 1.96

c.Z < -1.64 or Z > 1.64

Question 8

Based on the test-statistics and your chosen level of significance, what is your statistical inference?  

a.Reject the Null Hypothesis

b.Fail to Reject the Null Hypothesis

Question 9

The p-value of the above hypothesis test is 0.247. What is your statistical decision (previously, you chose a significance level of 10%)?

a. Reject the Null Hypothesis

b. Fail to Reject the Null Hypothesis

Question 10

Based on the statistical inference above, what is your business decision? In the past, your company did not expand to another country if the average income of the target market was different from the US. Group of answer choices

a.Expand to Netherlands

b.Do not expand to Netherlands

c.I am undecided

Question 11

If the actual average income of the Dutch target market is $43,000, then your statistical decision and subsequent business decision is an example of

Group of answer choices

a.Type I Error

b.Type II Error

c. No Error has been committed

Question 12

How would your statistical and subsequent business decision change if you use a 5% level of significance (instead of the 10% level of significance used above) Group of answer

a. choices Remains the same

b. Gets reversed

From two bags like A and B, A has 2 pink and 3 purple balls, B has 4 pink and 5 purple balls. A random ball is received from A. It is thrown to B and a random ball is drawn from B.

I- What is the probability that the Last drawn ball is purple?

II- What is the probability that the balls drawn from A and B are the same color?

Which of the following is true

4. Interpretation of simple linear regression

The linear model below explores a potential association between property damage and windspeed based on observational data from 94 hurricanes that hit the United States between 1950 and 2012. The variables are

Damage: property damage in millions of U.S. dollars (adjusted for inflation to 2014) for each hurricane

Landfall.Windspeed: Maximum sustained windspeed in miles per hour measured along U.S. coast for each hurricane

* Assume that the sample data satisfies all assumptions for linear regression.

Level of significance = 0.05.   

> summary(model)

Call:

lm(formula = Damage ~ Landfall.Windspeed)

Residuals:

   Min     1Q Median     3Q    Max

-9294 -4782 -1996   -531 90478

Coefficients:

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

(Intercept)                                -10041.78        6064.29          -1.656              0.1012

Landfall.Windspeed    142.07             56.65               2.508               0.0139 *

---

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

Residual standard error: 12280 on 92 degrees of freedom

Multiple R-squared: [ A ],      Adjusted R-squared: 0.05381

F-statistic: 6.289 on 1 and 92 DF, p-value: 0.01391

(a)   Write the equation for the linear model using the variables Damages and Landfall.Windspeed, taking the results of the t-tests into account.

(b) A hurricane is defined as a storm with windspeeds greater than 74 miles per hour. Interpret the value of the intercept in connection to the real-life context of this model (two or three sentences). Hint: Is the intercept truly meaningful, given the definition of a hurricane?

(c) The value of Pearson’s correlation coefficient for Damages and Landfall.Windspeed is 0.2529438. Calculate and interpret the value of R² , denoted [A] in the table, in relation to the predictor and response variables.

(d) The range of observed maximum windspeeds in the sample data is 75 – 190 miles per hour. Is it appropriate to use the linear model to predict the cost of damage for a hurricane with a maximum windspeed of 150 miles per hour? Why or why not? If so, estimate the typical value of damages (specifying units).

(e) Would it be appropriate to use the linear model to predict the cost of damage for a hurricane with a maximum windspeed of 225 miles per hour? Why or why not? If so, estimate the typical value of damages (specifying units).

Let X be a continuous random variable having a normal probability distribution with mean µ = 210 and standard deviation σ = 15.

(a) Draw a sketch of the density function of X.
(b) Find a value x∗ which cuts left tail of area 0.25 .
(c) Find a value y∗ which cuts right tail of area 0.30.
(d) Find a and b such that p(a ≤ X ≤ b) = 0.78.

Using the z table (The Standard Normal Distribution Table), find the critical value (or values) for the two-tailed test with

a=0.05

. Round to two decimal places, and enter the answers separated by a comma if needed.