A Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars) Determine if there is a significant linear correlation between advertising cost and profit Use a significance level of 0 01 and round all values to 4 decimal places Advertising Cost Profit 3 25 4 19 5 19 6 21 7 17 8 20 Ho 0 Ha 0 Find the Linear Correlation Coefficient r Find the p value p value The p value is Less than (or equal to) Greater than The p value leads to a decision to Reject Ho Accept Ho Do Not Reject Ho The conclusion is There is a significant linear correlation between advertising expense and profit There is a significant negative linear correlation between advertising expense and profit There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit There is a significant positive linear correlation between advertising expense and profit B A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year The results of the survey are shown below Vacation Days 13 7 7 10 5 11 15 6 1 15 11 Sick Days 1 5 1 0 3 4 0 3 10 0 3 Find the correlation coefficient r r Round to 2 decimal places The null and alternative hypotheses for correlation are H0 H0 r 0 H1 H1 r 0 The p value is (Round to four decimal places) Use a level of significance of 0 05 0 05to state the conclusion of the hypothesis test in the context of the study There is statistically significant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken Thus, the regression line is useful There is statistically significant evidence to conclude that an employee who takes more vacation days will take fewer sick days than an employee who takes fewer vacation days There is statistically significant evidence to conclude that an employee who takes more vacation days will take more sick days than an employee who takes fewer vacation days There is statistically insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken Thus, the use of the regression line is not appropriate r2 (Round to two decimal places) Interpretr2 There is a 59 chance that the regression line will be a good predictor for the number of sick days taken based on the number of vacation days taken There is a large variation in the number of sick days employees take, but if you only look at employees who take a fixed number of vacation days, this variation on average is reduced by 59 Given any group with a fixed number of vacation days taken, 59 of all of those employees will take the predicted number of sick days 59 of all employees will take the average number of sick days 6 The equation of the linear regression line is y x (Please show your answers to two decimal places) 7 Use the model to predict the number of sick days taken for an employee who took 4 vacation days this year Sick Days (Please round your answer to the nearest whole number ) 8 Interpret the slope of the regression line in the context of the question For every additional vacation day taken, employees tend to take on average 0 52 fewer sick days As x goes up, y goes down The slope has no practical meaning since a negative number cannot occur with vacation days and sick days 9 Interpret the y intercept in the context of the question If an employee takes no vacation days, then that employee will take 7 sick days The best prediction for an employee who doesn't take any vacation days is that the employee will take 7 sick days The y intercept has no practical meaning for this study The average number of sick days is predicted to be 7 C A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout The results of the survey are shown below Seeds Produced 68 62 67 68 46 57 48 48 68 Sprout Percent 52 64 65 5 62 76 52 5 66 69 50 a Find the correlation coefficient 7 Round to 2 decimal places b The null and alternative hypotheses for correlation are Ho 0 H1 O The p value is (Round to four decimal places) c Use a level of significance of o 0 05 to state the conclusion of the hypothesis test in the context of the study There is statistically insignificant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds There is statistically significant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout Thus, the regression line is useful There is statistically significant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds There is statistically insignificant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout Thus, the use of the regression line is not appropriate d (Round to two decimal places) e Interpret 72 There is a 45 chance that the regression line will be a good predictor for the percent of seeds that sprout based on the number of seeds produced OThere is a large variation in the percent of seeds that sprout, but if you only look at plants that produce a fixed number of seeds, this variation on average is reduced by 45 Given any group of plants that all produce the same number of seeds, 45 of all of these plants will produce seeds with the same chance of sprouting 45 of all plants produce seeds whose chance of sprouting is the average chance of sprouting

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A. Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if

A. Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant linear correlation between advertising cost and profit . Use a significance level of 0.01 and round all values to 4 decimal places.

Advertising Cost	Profit
3	25
4	19
5	19
6	21
7	17
8	20

Ho:? = 0 Ha:? ? 0

Find the Linear Correlation Coefficient r = __________

Find the p-value p-value = ________

The p-value is

Less than (or equal to) ??
Greater than ??

The p-value leads to a decision to

Reject Ho
Accept Ho
Do Not Reject Ho

The conclusion is

There is a significant linear correlation between advertising expense and profit.
There is a significant negative linear correlation between advertising expense and profit.
There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit.
There is a significant positive linear correlation between advertising expense and profit.

B. A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below.

Vacation Days	13	7	7	10	5	11	15	6	1	15	11
Sick Days	1	5	1	0	3	4	0	3	10	0	3

Find the correlation coefficient: r=r= Round to 2 decimal places.
The null and alternative hypotheses for correlation are: H0:H0: ? r ? ? == 0 H1:H1: ? ? ? r ??0 The p-value is: __________ (Round to four decimal places)
Use a level of significance of?=0.05?=0.05to state the conclusion of the hypothesis test in the context of the study.
- There is statistically significant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the regression line is useful.
- There is statistically significant evidence to conclude that an employee who takes more vacation days will take fewer sick days than an employee who takes fewer vacation days .
- There is statistically significant evidence to conclude that an employee who takes more vacation days will take more sick days than an employee who takes fewer vacation days.
- There is statistically insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the use of the regression line is not appropriate.
r2=__________ (Round to two decimal places)
Interpretr2:

There is a 59% chance that the regression line will be a good predictor for the number of sick days taken based on the number of vacation days taken.
There is a large variation in the number of sick days employees take, but if you only look at employees who take a fixed number of vacation days, this variation on average is reduced by 59%.
Given any group with a fixed number of vacation days taken, 59% of all of those employees will take the predicted number of sick days.
59% of all employees will take the average number of sick days.
6. The equation of the linear regression line is: ?y=_______ +______ x (Please show your answers to two decimal places) 7. Use the model to predict the number of sick days taken for an employee who took 4 vacation days this year. Sick Days = _________ (Please round your answer to the nearest whole number.)
8. Interpret the slope of the regression line in the context of the question:
For every additional vacation day taken, employees tend to take on average 0.52 fewer sick days.
As x goes up, y goes down.
The slope has no practical meaning since a negative number cannot occur with vacation days and sick days.
9. Interpret the y-intercept in the context of the question:
If an employee takes no vacation days, then that employee will take 7 sick days.
The best prediction for an employee who doesn't take any vacation days is that the employee will take 7 sick days.
The y-intercept has no practical meaning for this study.
The average number of sick days is predicted to be 7.

C. A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below.

Seeds Produced 68 62 67 68 46 57 48 48 68 Sprout Percent 52 64 65.5 62 76 52.5 66 69 50 a. Find the correlation coefficient: 7 Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? ~ = 0 H1 : ? ~ O The p-value is: (Round to four decimal places) c. Use a level of significance of o = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically insignificant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds. There is statistically significant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the regression line is useful. There is statistically significant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds. There is statistically insignificant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the use of the regression line is not appropriate. d. (Round to two decimal places) e. Interpret 72 : There is a 45% chance that the regression line will be a good predictor for the percent of seeds that sprout based on the number of seeds produced. OThere is a large variation in the percent of seeds that sprout, but if you only look at plants that produce a fixed number of seeds, this variation on average is reduced by 45%%. Given any group of plants that all produce the same number of seeds, 45% of all of these plants will produce seeds with the same chance of sprouting. 45%% of all plants produce seeds whose chance of sprouting is the average chance of sprouting.