For each of the following scenarios, develop a testable hypothesis.
a. Scenario 1. Kelly and Jack are playing in the park. Jack rolls a marble
down the small playground slide. Kelly proposes the idea that the marble
would travel at a faster pace if it is rolled down the longer slide.
b. Scenario 2. Andy’s nightly chores include washing the family dishes. His
mother tends to cook everything that she prepares a bit too long. Because
of this, Andy spends a lot of swear, effort, and time washing the dishes.
He sees a commercial on televisions that claims that brand X dishwashing
detergent cuts through grease better than its competitor brand Y.
c. Scenario 3. Ali’s favorite food is microwave popcorn. She lives microwave
popcorn so much that she can’t stand to waste the un-popped kernels in
the bottom of the bag. The next time Ali goes to the grocery store she
buys all the brands of microwave popcorn that the store has.

Suppose a carnival director in a certain city imposes a patron height limit on an amusement park ride called Terror Mountain, due to safety concerns. Patrons must be at least 4 feet tall to ride Terror Mountain. Suppose patrons’ heights in this city follow a Normal distribution with a mean of 4.4 feet and a standard deviation of 0.8 feet (patrons are mostly children). Note: make sure to show all of your work in this question. Show the distribution that your random variable follows; state the probability you are asked to calculate; show any tricks you use; show how you standardize, show your rounded z-score (round to 2 decimal places), and state your found value from Table A4.

a) What is the probability that a randomly selected patron would be tall enough to ride Terror Mountain? [5 marks]

b) A group of 3 friends want to ride Terror Mountain. What is the probability that their mean height is greater than 4.5 feet? [5 marks]

Let's think about drug addiction and how American society treats individuals that have addiction problems. When someone is labeled a drug addict, they're identified by their problem and not as an individual. I thought this video provides an interesting alternative to our current policies.  

Drug related arrests are also disproportionate if we examine factors such as race and income level. The speaker discusses the "war on drugs" and how it has not been very effective in combating drug addiction and drug use.  

1. Do you think the war on drugs has been effective?

2. The speaker discusses two experiments on mice, one on solitude and one in "rat park". How are the results different in each experiment? How can we apply these two circumstances to human life?

3. What do you think are better solutions to reducing the rates of drug addiction.  

4. What programs can help individuals recovering from drug addiction reconnect with society?

Project 2: Capital Budgeting Activity
Scenario:
Your client owns a successful restaurant in downtown Chicago (at least pre-Covid-19!). She wants to open a second restaurant in the suburbs and has asked you to help her choose between two locations. Key information is listed below. Using the four capital budgeting methods that we know, prepare a presentation that shows your recommendation to your client (and why).

Initial Investment: 2,500,000 and use 9% discount rate

Annual non-cash (all depreciation) expenses:
Use straight line depreciation to find!
For both, assume no residual value and: 9% discount rate

REQUIREMENTS:

Calculate the following and note each formula

1. Payback Period
2. NPV
3. Internal Rate of Return Method
4. Profitability Index

1.At takeoff a commercial jet has a 65.0 m/s speed. Its tires have a diameter of 0.700 m.

(a) At how many rpm are the tires rotating?
___ rpm
(b) What is the centripetal acceleration at the edge of the tire?
____ m/s²
(c) With what force must a determined 10^-15 kg bacterium cling to the rim?
____N
(d) Take the ratio of this force to the bacterium's weight.
____(force from part (c) / bacterium's weight)

2.(a) A 19.0 kg child is riding a playground merry-go-round that is rotating at 35.0 rpm. What centripetal force must she exert to stay on if she is 1.00 m from its center?
____ N
(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rpm if she is 6.00 m from its center?
____ N
(c) Compare each force with her weight.
____ (force from part (a) / weight)
____ (force from part (b) / weight

Consider the following data between number of visitors x and the amount of wildlife seen in Cheaha State Park y,

(a) Find the mean of x and the mean of y.

(b) Find the standard deviation of x and the standard deviation of y. Use Excel.

(c) Find the correlation coefficient. Use Excel. (d) Find the slope and intercept of the linear regression line. Then write down the line.

(e) Make predictions for all the values of x in the table. Then calculate the residuals.

(f) Calculate the sum of squared residuals. (g) Calculate the standard deviation of the regression.

(h) Using the mean of x and your data for x, calculate the sum of squared deviations.

(i) Write down an appropriate null and alternative hypothesis.

(j) Calculate the test-statistic.

(k) Make a prediction for when x is 470, and calculate (xp − ¯ x)2. Then make a confidence interval around your prediction.

1. Old Billie is very excited for Letecia, but she is also worried about her. So she conducts a poll of 400 Avocado Park residents who have gone on a first date in the last month and asks them if they are glad they did. Old Billie has decided that she will stop the date from happening if there is less than a 75% chance that Letecia will be happy. Hadey tells her she is being extra, so she settles on a significance level of 0.01 to be safe.
   1. Identify the population of interest.
   2. Identify the variable of interest. What type of variable is it?
   3. What would be a suitable parameter for summarizing the variable you identified in part b?
   4. Write appropriate null and alternative hypotheses for Old Billie’s research goals.
   5. What assumptions must you make to perform a test on the null hypothesis you chose in part d?
   6. Calculate the P-Value and make a decision about the null hypothesis based on it.
   7. Summarize your decision from part f.

A.) A telephone manufacturer finds that the life spans of its telephones are normally distributed, with a mean of 6.7 years and a standard deviation of 0.5 year. (Round your answers to three decimal places.)

What percent of its telephones will last at least 7.25 years?

What percent of its telephones will last between 5.8 years and 6.8 years?

What percent of its telephones will last less than 6.9 years?

B.) The amount of time customers spend waiting in line at the ticket counter of an amusement park is normally distributed, with a mean of 6.5 min and a standard deviation of 1 min.

Find the z-score for the following data value 8 min.

Find the probability that a customer will wait less than 8 minutes. (Round your answer to three decimal places.)

Find the z-score for the following data value 6 min.

Find the probability that a customer will wait less than 6 minutes. (Round your answer to three decimal places.)

The following table shows age distribution and location of a random sample of 166 buffalo in a national park.

Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.

(a) What is the level of significance?

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State the null and alternate hypotheses.

H0: Age distribution and location are independent.

H1: Age distribution and location are not independent.

H0: Age distribution and location are not independent.

H1: Age distribution and location are not independent.

H0: Age distribution and location are not independent.

H1: Age distribution and location are independent.

H0: Age distribution and location are independent.

H1: Age distribution and location are independent.  

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

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