question 1

An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that express volume as a function of the mass. Round your answers to 3 decimal places

grams	Volume in ml
19	171.6
20.5	179.6
22	194.7
23.5	210.1
25	223.5
26.5	234.5
28	245.3

Volume = + where x is the grams of the unknown metal

Question 2

The table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a linear model that express Vitamin C content as a function of the weight of the Raspberries.

grams	Vitamin C content in mg
55	11.6
60	14.3
65	16.4
70	18.5
75	21.2
80	22.5
85	25.3

A) Find the regression equation: = + Round your answers to 3 decimal places

B) Answer the following questions using your un-rounded regression equation.

If we test 115 grams of raspberries what is the expected Vitamin C content? (round to the nearest tenth)

Question 3

Gotham City is piloting a crime reduction program so that it does not have to rely on the help of super-heroes anymore. The table below shows the number of crimes committed every year (since 2005). The mayor of Gotham needs your help and you are tasked to find the following:

Years ()	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014
Crimes ()	1368	1352	1337	1328	1324	1309	1328	1307	1302	1311

Use the data to create an appropriate linear function (in equation form) that represents the number of crimes as a function of the calendar year. Also, give the and 2 values from your calculator. Regression Equation: = 2 = Round all values to 3 decimal places. Gotham can stop relying on super-heroes' help once the number of crimes drop below 800 per year. In which year will that happen?

Question 4

The table below shows , the number of thousands of state-registered automatic weapons and , the number of murders per 100,000 residents for several Northwestern states.

	11.8	8.2	7.1	3.5	2.3	2.5	2.5	0.6
	13.9	11.2	9.8	6.9	5.9	6.5	6.2	4.7

Use your calculator to do a linear regression expressing the number of murders per 100,000 residents as a function of the number of thousands of state-registered automatic weapons. Also, give the and 2 values from your calculator Regression Equation: = 2 = Round to 3 decimal places. Using your linear regression, how many murders per 100,000 residents can be expected in a state with 7400 automatic weapons? Round to 3 decimal places. Using your linear regression, how many automatic weapons would be expected in a city with 6.3 murders per 100,000 residents? Round to the nearest whole weapon.

Question 5

The correlation coefficientfor two sets of data describes how strong the relationship is between two comparable data sets, or more specifically, "How strongly does the explanatory variable affect the response variable?" Can you come up with a real-world example of two data sets that have a correlation coefficient that would be close to negative one? (Briefly explain in words)

Question 6

Goodness of Fit Chi-Squared hypothesis test ( = 0.05) for the claim that all 6 outcomes of rolling 1 dice are equally likely. The sum of the observed outcomes = 88 Enter the expected value for each possible outcome the table; round these expected values to 1 decimal place

X	1	2	3	4	5	6
Observed Frequency (counts)	11	19	8	16	16	18
Expected Frequency (counts)

What is the chi-square test-statistic for this data? (Report answer accurate to 1 decimal places.) 2= What is the p-value for this sample? (Report answer accurate to 3 decimal places.) p-value = The p-value is...

• Less than
• Greater than This P-Value leads to a decision to...
• Reject the null hypothesis.
• Fail to reject the null hypothesis.

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that all 6 categories are equally likely to be selected.
• There is not sufficient evidence to warrant rejection of the claim that all 6 categories are equally likely to be selected.

Question 7

You want to see if it makes a difference which lane to be in when there is traffic. You randomly observe 296 cars as they pass by on the four lane freeway. The results are displayed in the table below. Use a level of significance of= 0.10.

1. Complete the rest of the table by filling in the expected frequencies:

Outcome	Frequency	Expected Frequency
Lane 1	74
Lane 2	65
Lane 3	65
Lane 4	92

1. What is the correct statistical test to use? Select an answer Homogeneity Independence Goodness-of-Fit Paired t-test
2. What are the null and alternative hypotheses? 0: 1:
3. The degrees of freedom =
4. The test-statistic for this data = (Please show your answer to three decimal places.)
5. The p-value for this sample = (Please show your answer to four decimal places.)
6. The p-value is Select an answer less than (or equal to) greater than
7. Based on this, we should Select an answer fail to reject the null accept the null reject the null
8. Thus, the final conclusion is...
   • There is sufficient evidence to conclude that the distribution of traffic is not uniform.
   • There is sufficient evidence to conclude that the distribution of traffic is uniform.
   • There is insufficient evidence to conclude that traffic and lanes are dependent.
   • There is insufficient evidence to conclude that the distribution of traffic is not uniform.
   • There is sufficient evidence to conclude that traffic and lanes are dependent

• The distribution of traffic is uniform.
• The traffic and lanes are independent.
• The traffic and lanes are dependent.
• The distribution of traffic is not uniform.
• The traffic and lanes are independent.
• The distribution of traffic is uniform.
• The traffic and lanes are dependent.
• The distribution of traffic is not uniform.

Question 8

You want to see if a card dealer is favoring one suit over another. You observe the dealer pick a card, put it back in the deck, shuffle, and then repeat the process 300 times. The results are displayed in the table below. Use an= 0.10significance level.

1. Complete the rest of the table by filling in the expected frequencies:

Outcome	Frequency	Expected Frequency
Spades	53
Hearts	74
Diamonds	86
Clubs	87

1. What is the correct statistical test to use? Select an answer Independence Goodness-of-Fit Paired t-test Homogeneity
2. What are the null and alternative hypotheses? 0: 1:
3. The degrees of freedom =
4. The test-statistic for this data = (Please show your answer to three decimal places.)
5. The p-value for this sample = (Please show your answer to four decimal places.)
6. The p-value is Select an answer greater than less than (or equal to)
7. Based on this, we should Select an answer accept the null fail to reject the null reject the null
8. Thus, the final conclusion is...
   • There is sufficient evidence to conclude that the distribution of suits is uniform.
   • There is insufficient evidence to conclude that the distribution of suits is not uniform.
   • There is sufficient evidence to conclude that the distribution of suits is not uniform.
   • There is sufficient evidence to conclude that suits and cards are dependent.
   • There is insufficient evidence to conclude that suits and cards are dependent.

• The suits and cards are independent.
• The suits and cards are dependent.
• The distribution of suits is uniform.
• The distribution of suits is not uniform.
• The distribution of suits is not uniform.
• The distribution of suits is uniform.
• The suits and cards are dependent.
• The suits and cards are independent.

Please answer the questions sequentially. Thank you.