To study how social media may influence the products consumers​ buy, researchers collected the opening weekend box office revenue​ (in millions of​ dollars) for 23 recent movies and the social media message rate​ (average number of messages referring to the movie per​ hour). The data are available below. Conduct a complete simple linear regression analysis of the relationship between revenue​ (y) and message rate​ (x).

Click the icon to view the data.

Message_Rate   Revenue_($millions)
1369.4 145
1217.5 76
575.9 70
308.1 36
453.2 35
292.7 34
245.8 21
675.6 19
150.8 19
162.2 19
111.1 18
146.2 17
417.2 16
95.5 16
103.6 15
119.8 15
73.8 15
84.8 14
122.3 9
58.9 8
146.4 7
37.5 2
3.9 1

a.The least squares regression equation is y equals=nothing+ (nothing) x

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

b. Determine the estimate of the standard deviation.

s=nothing

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

c. Identify the test statistic for the​ hypotheses, rounding to two decimal places.

t= nothing

d.Identify the p-value.

e.Compute fro r2

f.Use technology to create a​ 95% confidence interval for the slope β1​, rounding to three decimal places

The average American girl purchases 5.5 pairs of sports shoes. Suppose a sample of 64 customers is surveyed and the population standard deviation of shoes purchased is 2.3.

What is the standard error of the mean in the experiment?

2)

The average American girl purchases 5.5 pairs of sports shoes. Suppose a sample of 64 customers is surveyed and the population standard deviation of shoes purchased is 2.3.

What is the probability that the difference between the sample mean and population mean is less than 0.2?

3)

The average American girl purchases 5.5 pairs of sports shoes. Suppose a sample of 64 customers is surveyed and the population standard deviation of shoes purchased is 2.3.

What is the likelihood that the sample mean calculated is less than 5?

4)

The average American girl purchases 5.5 pairs of sports shoes. Suppose a sample of 64 customers is surveyed and the population standard deviation of shoes purchased is 2.3.

What is the probability that the sample mean is between 5 and 6 pairs of shoes?

A pediatrician wants to determine the relation that may exist between a​ child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. A normal probability plot suggests that the residuals are normally distributed. Complete parts​ (a) and​ (b) below.

Height_(inches)_-_x   Head Circumference_(inches)_-_y
27.75   17.6
27   17.5
27.5   17.5
25.5   17.1
25   16.9

​(a) Use technology to determine sb1.

sb1=__?__  

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

​(b) Test whether a linear relation exists between height and head circumference at the α=0.01 level of significance. State the null and alternative hypotheses for this test.

Choose the correct answer below.

A.

H0​: β0=0

H1​: β0>0

B.

H0​: β1=0

H1​: β1≠0

C.

H0​: β0=0

H1​: β0≠0

D.

H0​: β1=0

H1​: β1>0

Determine the​ P-value for this hypothesis test.

​P-value=__?__

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

What is the conclusion that can be​ drawn?

A.

Do not reject H0 and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance α=0.01.

B.

Reject H0 and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance α=0.01.

C.

Reject H0 and conclude that a linear relation does not exist between a​ child's height and head circumference at the level of significance α=0.01.

D.

Do not reject H0 and conclude that a linear relation does not exist between a​ child's height and head circumference at the level of significance α=0.01.

A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. A normal probability plot suggests that the residuals are normally distributed. Complete parts (a) and (b) below.

(a) Use technology to determine sb1

sb1= ______

(Round to four decimal places as needed)

(b) Test whether a linear relation exists between height and head circumference at the a=0.10 level of significance. State the null and alternative hypotheses for this test.

A) H0: B1=0

H1: B1 =/ (not equal) 0

B) H0: B0=0

H1: B0>0

C) H0:B0=0

H1: B0 =/ (not equal) 0

D) H0: B1=0

H1: B1 > 0

Determine the P-value for this hypothesis test.

P-value is ______ (Round to three decimal places as needed)

What is the conclusion that can be drawn?

A) Do not reject H0 and conclude that a linear relation exists between a childs height and head circumference at the level of significance a=0.01

B) Reject H0 and conclude that a linear relation exists between a childs height and head circumference at the level of significance a=0.01

C) Reject H0 and conclude that a linear relation does not exist between a childs height and head circumference at the level of significance a=0.01

D) Do not reject H0 and conclude that a linear relation does not exist between a childs height and head circumference at the level of significance a=0.01

What are some ways that a company can track accounts receivable to ensure that customers are paying on time. What are some consequences of a customer not paying the balance owed on accounts receivable? Please provide three specific consequences.

What is microfinance, and how can it contribute to economic growth?

What are four processes that contribute to transpiration in a tall tree?

How does auditing contribute to better financial reporting?

How do accounting professionals contribute to practices of sustainability?