The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based on this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x,  for using the completion percentage to predict the interception percentage for an NFL quarterback. 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.

2 of 6

3 of 6

4 of 6

5of 6

6 of 6

A marketing survey of 200 random adult Americans found that 78 had Amazon Prime accounts, 49 had Netflix Accounts, and 21 had Hulu accounts. 8 adults had all three accounts, while 12 had both Netflix and Hulu, 10 had both Hulu and Amazon Prime, and 25 had both Amazon Prime and Netflix.

(a) How many adults in the survey had none of the three services mentioned? (b) How many adults in the survey had only Amazon Prime?

(c) How many adults in the survey had exactly two of the services mentioned? (d) Of the adults who owned Amazon Prime, how many also owned Hulu?
(e) Of the adults who owned Hulu, how many also owned Amazon Prime?

(f) Are owning Amazon Prime and Hulu independent events in this study? Explain your answer.

Seven people are in an elevator which stops at ten floors. In how many ways can they get off the elevator?

10^7

C(10,7)

7^10

P(10,7)

A hiking group consists of 12 students and 2 leaders. A leader must be at the front and back of the line. How many ways can the group hike in a line?

14!

12!*2!

14!/2!

12!

n a test of the effectiveness of garlic for lowering​ cholesterol, 8181 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes​ (before minus​ after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 0.30.3 and a standard deviation of 18.218.2. Use a 0.010.01 significance level to test the claim that with garlic​ treatment, the mean change in LDL cholesterol is greater than 00. What do the results suggest about the effectiveness of the garlic​ treatment? Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative​ hypotheses? A. Upper H 0H0​: muμequals=00 ​mg/dL Upper H 1H1​: muμnot equals≠00 ​mg/dL B. Upper H 0H0​: muμequals=00 ​mg/dL Upper H 1H1​: muμgreater than>00 ​mg/dL C. Upper H 0H0​: muμgreater than>00 ​mg/dL Upper H 1H1​: muμless than<00 ​mg/dL D. Upper H 0H0​: muμequals=00 ​mg/dL Upper H 1H1​: muμless than<00 ​mg/dL Determine the test statistic. nothing ​(Round to two decimal places as​ needed.) Determine the​ P-value. nothing ​(Round to three decimal places as​ needed.) State the final conclusion that addresses the original claim. ▼ Reject Fail to reject Upper H 0H0. There is ▼ not sufficient sufficient evidence to conclude that t

In the following statements f(theta; x) is the likelihood function. Select which of the following are true statements about maximum likelihood estimates (MLE's).

Hint: In general, maximizing a function f(x) is equivalent to minimizing -f(x).

Group of answer choices

MLE's are unbiased.

MLE's minimize the negative log likelihood function, -log(f(theta; x))

MLE's are always easy to find.

MLE's maximize the likelihood function f(theta; x).

MLE's are not affected by outliers in the data.

There are 15 light bulbs of which 5 are defective. In how many ways can six light bulbs with exactly one defective be chosen?

C(15,6)

C(10,5)*C(5,1)

P(10,5)*P(5,1)

P(15,6)

How many ways are there to fill out a 25 question multiple choice exam if there are 5 ways to answer each question?

25⁵

5²⁵

C(25,5)

^P(25,5)

How many nonnegative solutions (x_i >=0 for 1<=i<=3) does the equation x₁ + x₂ + x₃ = 10 have?

10³

C(10,3)

C(12,2)

3¹⁰

Teams A and B play in a basketball tournament. The first team to win two games in a row or a total of three games wins the tournament. What is the number of ways the tournament can occur?

14

12

8

10

How many different rearrangements are there of the letters in the word BUBBLE?

60

100

120

80

How many ways are there to arrange all the words in this tongue twister?
CAN YOU CAN A CAN AS A CANNER CAN CAN A CAN?

12!/(6!*3!)

12!

12!/3!

12!/6!

Twelve points are located on the circumference of a circle. Lines are drawn to connect all possible pairs of points. How many lines are drawn?

66

144

132

24

Consider the following study results concerning Age and Church Attendance:

                                                                                                Age

Church Attendance         20-29                     30-39                     40-49                     50-59

Yes 21                           63                           94                           72

No 69                           87                           106                         78

Test to see if the proportion of people who attend church is the same for all age groups (95% confidence).

Using the Marascuillo Pairwise comparison procedure, test for a difference in proportions between the 30-39 and 40-49 age groups.

What is the Critical Value (CV)?

What is your decision about the null (Ho: P2=P3) and your conclusion

Son's Height   Father's Height
64.4 79
69.2 67.1
76.4 70.9
69.2 66.8
78.2 72.8
76.9 70.4
71.8 70.3
79 70.1
75.8 79.5
72.3 65.5
69.2 65.4
66.9 69.1
64.5 74.5

To test the claim that sons are taller than their fathers on average, a researcher randomly selected 13 fathers who have adult male children.  She records the height of both the father and son in inches.  

Note: to answer the questions below, subtract (Son’s Height – Father’s Height).

1. What is (are) the parameter(s) of interest?  Choose one of the following symbols m(the population mean);m_D(the mean difference from paired (dependent) data);m₁- m₂ (the difference of two independent means) and describe the parameter in context of this question in one sentence.

2. Depending on your answer to part (a), construct one or two relative frequency histograms.  Remember to properly title and label the graph(s).  Copy and paste these graphs into your document.

3. Describe the shape of the histogram(s) in one sentence.

4. Depending on your answer to part (a), construct one or two boxplots and copy and paste these graphs into your document.

5. Does the boxplot (or do the boxplots) show any outliers?  Answer this question in one sentence and identify any outliers if they are present.

6. Considering your answers to parts (c) and (e), is inference appropriate in this case?  Why or why not?  Defend your answer using the graphs in two to three sentences.

Consider the following study results concerning Age and Church Attendance:

                                                                                                Age

Church Attendance         20-29                     30-39                     40-49                     50-59

Yes 21                           63                           94                           72

No 69                           87                           106                         78

Test to see if the proportion of people who attend church is the same for all age groups (95% confidence).

What is the value of the test statistic?

What is the p-value?

What is your decision concerning the null hypothesis and your conclusion?

Let estimator π(hat) = X(bar) for X1, X2, . . . , X_n, X_i ∼ Bernoulli(π)

Recall: P(X = x) = π^x (1 − π)^1−x , x ∈ {0, 1}

E(X) = π

V(X) = π(1 − π)

a. Show that π(hat) is a Consistent estimator of π

b. Find the Maximum Likelihood Estimator of π

c. Show that π(hat) is a Minimum Variance Unbiased Estimator of π

Please explain the answer in detail

In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in television ads in the United States and in the United Kingdom. Suppose that independent random samples of television ads are taken in the two countries. A random sample of 400 television ads in the United Kingdom reveals that 143 use humor, while a random sample of 500 television ads in the United States reveals that 126 use humor.

(a) Set up the null and alternative hypotheses needed to determine whether the proportion of ads using humor in the United Kingdom differs from the proportion of ads using humor in the United States.

(b) Test the hypotheses you set up in part a by using critical values and by setting α equal to .10, .05, .01, and .001. How much evidence is there that the proportions of U.K. and U.S. ads using humor are different? (Round the proportion values to 3 decimal places. Round your answer to 2 decimal places.)

(c) Set up the hypotheses needed to attempt to establish that the difference between the proportions of U.K. and U.S. ads using humor is more than .05 (five percentage points). Test these hypotheses by using a p-value and by setting α equal to .10, .05, .01, and .001. How much evidence is there that the difference between the proportions exceeds .05? (Round the proportion values to 3 decimal places. Round your z value to 2 decimal places and p-value to 4 decimal places.) (d) Calculate a 95 percent confidence interval for the difference between the proportion of U.K. ads using humor and the proportion of U.S. ads using humor. Interpret this interval. Can we be 95 percent confident that the proportion of U.K. ads using humor is greater than the proportion of U.S. ads using humor? (Round the proportion values to 3 decimal places. Round your answers to 4 decimal places.)

Suppose you wish to find out the answer to the questions “Do Americans prefer Coke or Pepsi?” You conduct a blind taste test in which individuals are randomly asked to drink one of the colas first, followed by the other cola, and then asked to disclose which drink they prefer. The results of your taste test indicate that 53 of 100 individuals prefer Pepsi. Conduct a hypothesis test to determine if more than 50% of people prefer Pepsi to coca-cola. Use the ? = 0.05 level of significance.

a. Using alphaαequals=​0.01, perform a​ chi-square test to determine if the proportion of households without health insurance differs by income bracket.

Choose the correct null and alternative hypotheses below.

A.

Upper H 0H0​:

Not all​ p's are equal

Upper H 1H1​:

p 1 equals p 2 equals p 3 equals p 4p1=p2=p3=p4

B.

Upper H 0H0​:

p 1 equals p 2 equals p 3 equals p 4p1=p2=p3=p4

Upper H 1H1​:

p 1 not equals p 2 not equals p 3 not equals p 4p1≠p2≠p3≠p4

C.

Upper H 0H0​:

p 1 not equals p 2 not equals p 3 not equals p 4p1≠p2≠p3≠p4

Upper H 1H1​:

p 1 equals p 2 equals p 3 equals p 4p1=p2=p3=p4

D.

Upper H 0H0​:

p 1 equals p 2 equals p 3 equals p 4p1=p2=p3=p4

Upper H 1H1​:

Not all​ p's are equal

What is the test​ statistic?

chi squaredχ2equals=nothing

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

What is the critical​ value?

chi Subscript 0.01 Superscript 2χ20.01equals=nothing

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

State the conclusion.

▼

Do not reject

Reject

Upper H 0H0.

There is

▼

sufficient

insufficient

evidence that the proportion of households without health insurance differs by income bracket.

b. Interpret the meaning of the​ p-value.

What is the​ p-value?

​p-valueequals=nothing

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

What does the​ p-value mean? Select the correct choice and fill in the answer box to complete your choice.

​(Round to one decimal place as​ needed.)

A.There is a

nothing​%

chance of observing a test statistic value greater than the actual test statistic value if there is no difference in the proportion of households without health insurance.

B.There is a

nothing​%

chance of rejecting the null hypothesis when it should not be rejected.

C.Given a very large number of​ samples, there is a

nothing​%

chance of observing a sample with the given data.

c. How does income appear to impact the likelihood that a household has insurance​ coverage?

A.

The proportion of households without health insurance is always uniform and does not depend on income bracket.

B.The proportion of households without health insurance

does not differdoes not differ

by income bracket.

C.

The proportion of households without health insurance increases as income increases.

D.The proportion of households without health insurance

differs by income bracket.

Click to select your answer(s).