The medical reports from the track team in university x showed that, over the last few years, its first-year athletes have had a resting heart rate of μ= 53 beats per minute, with σ= 10. What is the probability that this year the sample of freshman (n=25) have a mean heart rate of 57 or lower (M<=57)?

a. 2.28%

b. 34.5%

c. 97.7%

d. 65.6%

1. each Given the following data comes from the football program of a quaint university north of here that wears blue and yellow. Evaluate this data for linear regression:

1. Make a scatter plot
2. Which variable is the predictor or explanatory variable and which is the response variable?
3. Conduct a hypothesis test to determine if there is a significant linear correlation
   1. State your null and alternative hypothesis
   2. Justify rejecting or failing to reject the null at the .05 significance level.
4. Provide the equation
5. Determine r
6. What percent of the variation in points scored is accounted for by the regression equation?
7. Find the residual of 7 penalties.
8. Estimate the number of points scored if Quaint U is penalized 6 times in the game
9. Estimate the number of points scored if Quaint U is penalized 80 times in the game
10. Determine the 95% confidence interval for the slope coefficient
11. Sketch a plot of the standardized residuals on the vertical axis against y on the horizontal. Mark maximum and minimum values of the standardized residuals on y axis.

Suppose that salaries of recent graduates from a large state university are normally distributed with mean $45,000 and standard deviation $4,200. (1) What proportion of salaries are between $40,000 and $55,000? (2) What two salaries bound the middle 40%?

4. Later this year, a team from Technion University in Israel is planning to launch three small satellites as part of their ongoing SAMSON project. The team will test the use of radiation pressure from sunlight, incident on a satellite’s solar panels, to provide the energy needed to increase the radius of the satellite’s orbit. To confirm the theoretical viability of this idea, consider a nanosatellite of mass 2.10 kg in a circular orbit around Earth with a period of 96.0 minutes. The satellite’s solar panels have and albedo of 20.0% and area of 0.200 m2 , and they are maintained in an orientation perpendicular to the incident sunlight for the quarter of the satellite’s orbit in which the satellite achieves the greatest linear displacement away from the sun. Find the increase in the radius of the satellite’s orbit after one day. (This is a work-energy problem. You will need to find the original radius of the orbit, and then consider the work done by the radiation force exerted on the solar panels, then relate this to the initial and final energy of the circular orbit.) Assume the intensity of sunlight is 1400 W/m2 . ANSWER IS 19 METERS

Researchers at the University of Maryland recorded body temperatures from a random sample of 93 healthy adults. They obtained a sample mean of 98.42 ℉ and a standard deviation of 0.65℉. Use this sample data to test the hypothesis that the mean body temperature of all healthy adults is actually less than 98.6℉.

A committee surveyed 173 students from a large university campus and found that 53 of them participated in varsity sports. (a) Based on the survey results, construct and interpret a 95% confidence interval for the proportion of students who are varsity athletes. (b) Based on the survey results, test the claim that more than 25% of students are varsity athletes. Use alpha=0.01α = 0.01. Show all work.

Shelli graduates from the University of South next month on her 25^th birthday, and she is excited to begin her new career. Because she wants to have a comfortable living when she retires, Shelli has decided to begin planning for her retirement now. As a result, she is currently evaluating the amount she needs to contribute to a retirement fund satisfy her financial requirements at retirement. After speaking to retired friends and relatives, Shelli estimates she will need $60,000 each year to be able to live comfortably and enjoy her “twilight years.” In addition, Shelli expects that she can invest in a retirement fund that will yield 8 percent interest compounded annually for a long as she contributes to the fund. As soon as she retires, Shelli will have to move her retirement “nest egg” to another investment so she can withdraw money when she needs it. Her plans are to move the money to a fund that allows withdrawals at the beginning of each year and pays 5 percent interest compounded annually. Shelli expects to retire in 40 years, and, after taking an online “life expectancy” quiz, she has concluded that she will live another 25 years after she retires. If Shelli’s expectations are correct, how much must she contribute to the retirement fund to satisfy her retirement plans if she intends to make her first contribution to the fund one year from today and the last contribution on the day she retires?

Alvin wants to save money to pay for his college education, which he plans to start in three years. Currently, the cost per year (for everything—food, clothing, tuition, books, transportation, and so forth) to attend the college he has chosen is $15,000; but these costs are expected to increase at the same rate as inflation, which is 3 percent, each year. Alvin plans to make three equal annual deposits into his “education” investment account beginning today. These deposits will earn 8 percent interest.

a.   If he plans to finish his college degree in four years, what will be the cost of Alvin’s education each year he is in college?

b.   How much must Alvin contribute each year so that he has enough money in his education fund when he starts college in three years to pay the costs for the four years it takes him to complete his degree?

Researchers from the university of Kent, UK, were interested in whether collectivist or individualist attitudes are related to one’s intent to comply with social distancing and safety guidelines during COVID-19. Participants were classified as either collectivist or individualist, and rated their intent to comply with guidelines on a scale from 1-5, where 1 is definitely not and 5 is definitely yes. Please conduct an independent-groups t test to determine if there is a significant difference in intention to comply between individualists and collectivists.

In addition, please:
- report cohen’s d
- report r^2
- conduct and interpret an F-MAX test
- include 95% confidence intervals
- report your answer in words that directly address the research question

Collective

x f

3 2

4 6

5 12

Individual

x f

1 1

2 3

3 11

4 13

5 2

Researchers from the University of Kent, UK, were interested in whether collectivist or individualist attitudes are related to one’s intent to comply with social distancing and safety guidelines during COVID-19. Participants were classified as either collectivist or individualist and rated their intent to comply with guidelines on a scale from 1-5, where 1 is definitely not and 5 is definitely yes. Please conduct an independent-groups t-test to determine if there is a significant difference in intention to comply between individualists and collectivists.

In addition, please:
- report cohen’s d
- report r^2
- conduct and interpret an F-MAX test
- include 95% confidence intervals
- report your answer in words that directly address the research question
- and show all work in step by step detail.

Collective

x f

3 2

4 6

5 12

Individual

x f

1 1

2 3

3 11

4 13

5 2

The opinion of university alumni is important. One question from a recent survey of 450 business alumni was, “Should foreign language be required of all undergraduate business majors?” The results of the study indicated that 30% of the sample were in favor of a foreign language requirement; 54% were opposed to a foreign language requirement; and the remainder were undecided. Do the survey results indicate that the majority of alumni do not support a foreign language requirement? Solve manually and then verify your results with PHStat. Include Type II error with your solution.