Statistics))

1.The Round-trip-time between the college and home for a student is normally distributed with a mean of 47 min and a standard deviation of 4.6 min. To one-decimal place, what Round-trip-time would be considered the 70th percentile? Make sure to include units.

2.A recent study showed that the average amount of time spent doing part time job by students at a college is 29 hours per week with a standard deviation of 3.8 hours. If 64 students were selected at random, what is the probability that their average weekly working hours will be less than 20 hours?Round answer to two decimals, if necessary.Express answer in percent. Don't forget to put % sign with you answer.

ACT Prep Course. ACT prep courses like to market that you can increase your ACT score by taking their courses. Some statisticians were curious how effective these courses really were. They decided to investigate the truth of the claim by measuring the average score increase for a random sample of students selected to take an ACT prep course. These students took the ACT twice, once before and once after taking the course. The variable of interest was the increase in scores between first and second attempts. NOTE: The population of interest is all students who took the ACT prep course.

(a) Identify µ in this scenario.

(Choose One)

• Average score of all people in the sample.

• True average increase in score of all people in the population

. • True average score of all people in the population.

• Average increase in score by all people in the sample

. (b) In order to test the researcher’s claim, identify the appropriate: i. null hypothesis – H0 : ii. alternative hypotheses – Ha :

1 (c) Suppose that an average increase in score of 3 points (x = 3) and standard deviation of s = 5.4 points were found in each of the following scenarios. Further, assume the difference in score is normally distributed. For each case, compute the degrees of freedom and test statistic and assess the strength of evidence against the null hypothesis. Round t-statistics to two decimals. i.

Scenario 1: a sample of size n = 9 A. t = with df = B. The p-value corresponding to the correct test statistic is 0.06673. Based on this p-value, there is... • little to no evidence against the null hypothesis.

• borderline/weak evidence against the null hypothesis.

• moderate evidence against the null hypothesis. •

substantial/strong evidence against the null hypothesis.

• overwhelming evidence against the null hypothesis.

ii. Scenario 2: a sample of size n = 24 A. t = with df = B. The p-value corresponding to the correct test statistic is 0.00611. Based on this p-value, there is... • little to no evidence against the null hypothesis.

• borderline/weak evidence against the null hypothesis.

• moderate evidence against the null hypothesis.

• substantial/strong evidence against the null hypothesis.

• overwhelming evidence against the null hypothesis.

iii. Scenario 3: a sample of size n = 444 A. t = with df = B. The p-value corresponding to the correct test statistic is <0.0001. Based on this p-value, there is...

• little to no evidence against the null hypothesis.

• borderline/weak evidence against the null hypothesis. •

moderate evidence against the null hypothesis. • s

substantial/strong evidence against the null hypothesis. •

overwhelming evidence against the null hypothesis.

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μ μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.4 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 500 . In answering the questions, use z ‑scores rounded to two decimal places. (a) If you choose one student at random, what is the probability that the student's score is between 495 and505 ? Use Table A, or software to calculate your answer. (Enter your answer rounded to four decimal places.) probability: (b) You sample 25 students. What is the standard deviation of the sampling distribution of their average score x¯ ? (Enter your answer rounded to two decimal places.) standard deviation: (c) What is the probability that the mean score of your sample is between 495 and 505 ? (Enter your answer rounded to four decimal places.) probability:

State the null and alternative hypotheses for each of the following situations. (That is, identify the correct number μ₀ and write H₀:μ=μ0 and the appropriate analogous expression for Ha.)

A.      The average July temperature in a region historically has been 74.5°F. Perhaps it is higher now.

B.      The average weight of a female airline passenger with luggage was 145 pounds ten years ago. The FAA believes it to be higher now.

C.      The average stipend for doctoral students in a particular discipline at a state university is $14,756. The department chairman believes that the national average is higher.

D.      The average room rate in hotels in a certain region is $82.53. A travel agent believes that the average in a particular resort area is different.

E.       The average farm size in a predominately rural state was 69.4 acres. The secretary of agriculture of that state asserts that it is less today.

*****YOU MUST SHOW ALL OF YOUR WORK TO DETERMINE HOW YOU ARRIVED AT THE SOLUTION IN ORDER TO RECEIVE CREDIT****

Round probabilities to four places. For example, 0.1234. Show your work. For example, if you are adding two probabilities you could do this: 7/59 + 9/59 = 16/59 = 0.2712.

1. You draw one card from a deck of 52 cards. If you get a heart, you win $18. If you get anything else, you pay $5. Note that there are 13 hearts in the deck.

What is the probability of winning the game?

What is the expected value of the game?

If you play the game 100 times, what is your expected gain or loss?

2. A class has sophomores and juniors, and biology and history majors. The table below shows the number of students in each category. There are 59 students in the class. (There are no double-majors.)

a) If one student is chosen at random, what is the probability of selecting a biology major?

b) If one student is chosen at random, what is the probability of selecting a biology major or a sophomore?

c) If two students are chosen at random, what is the probability of selecting a junior history major and then a sophomore biology major? The selections are made without replacement.

d) If one student is chosen at random, what is the probability of selecting a junior, given that the student chosen is a biology major?

e) If two students are chosen at random, what is the probability of selecting a sophomore history major and then another sophomore history major? The selections are made without replacement.

3. Find the following probabilities using the standard normal table:

a) P(z < 1.67)

b) P(z > -1.44)

c) P(-0.87 < z < 1.95)

4. A basketball player has made 65 of 79 free-throws attempted this season. What is the probability that the player will make the next free-throw they attempt?

What is the probability that the player makes their next 10 free-throws? Assume each free-throw is an independent event.

5. Horses in a stable have a mean weight of 950 pounds with a standard deviation of 77 pounds. Weights of horses follow the normal distribution. One horse is selected at random.

a) What is the probability that the horse weighs less than 900 pounds?

b) What is the probability that the horse weigh more than 1,100 pounds?

c) What is the probability that the horse weighs between 900 and 1,100 pounds?

d) What weight is the 90th percentile? (Round to the nearest pound)

6. Your aunt comes to you with an investment opportunity. She needs you to invest $500,000. If the investment succeeds, it will pay you back your investment plus an additional $2 million. If it fails, you get nothing back. She thinks there is a 30% chance of success.

What is the expected value of the investment?

What is the most likely outcome?

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 46 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.80 ml/kg for the distribution of blood plasma.

A: Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)

lower limit

upper limit

margin of error

B:What conditions are necessary for your calculations? (Select all that apply.)

σ is known

σ is unknown

n is large

the distribution of weights is uniform

the distribution of weights is normal

C:Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.60 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

male firefighters

a hypothesis was made that students would preform better at an optimal amount of playtime.

selected 3 classes to be given a certain amount of playtime per day

class 1, 30 minutes of play

class 2, 60 minutes of play

class 3, 120 minutes of play

after 3 months all classes were given standardized tests (n=28) and resulting analysis revealed that SS between=56 and SS total=542

a) what is the value of a1+a2+a3

b) what is the value of a1^2+a2^2+a3^2

c) what are the calculated and tabled values of the f statistic

f calc=

f tabled=

In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 26 out of 857 fish died when caught and released using barbless hooks on flies or lures. All hooks were removed from the fish.

(a) Let p represent the proportion of all pike and trout that die (i.e., p is the mortality rate) when caught and released using barbless hooks. Find a point estimate for p. (Use 4 decimal places.)


(b) Find a 95% confidence interval for p. (Use 4 decimal places.)

Give a brief explanation of the meaning of the interval.

5% of the all confidence intervals would include the true catch-and-release mortality rate.

95% of the confidence intervals created using this method would include the true catch-and-release mortality rate.   

95% of the all confidence intervals would include the true catch-and-release mortality rate.

5% of the confidence intervals created using this method would include the true catch-and-release mortality rate.

MY NOTES

How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds):

Assume that the population of x values has an approximately normal distribution.(a) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Find a 75% confidence interval for the population average weight μ of all adult mountain lions in the specified region. (Round your answers to one decimal place.)

The New York Times conducted a poll on women’s issues in June of 1989. One question asked was, “Many women have better jobs and more opportunities than they did 20 years ago. Do you think women have had to give up too much in the process, or not? Of the 1,033 women who were asked, 800 said “Yes.” Take these 1,033 women to be a simple random sample of all adult women. Calculate a 95% confidence interval for the proportion of all adult women who would say “Yes” to this statement using two decimal places.

What's the center of the interval?

What's the margin of error?

What's the lower bound of the interval?

What's the upper bound of the interval?

Password consists of five characters: one lowercase letter and four digits 0 – 9.

1. How many possible combinations for the password are there if digits can be repeated?
2. How many possible combinations for the password are there if digits can not be repeated?
3. What is a percentage of passwords with repeated digits?

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age 37 41 58 61 67 Bone Density 343 330 318 314 312 Table Step 1 of 6 : Find the estimated slope. Round your answer to three decimal places.

In a championship series, the winner emerges by winning 5 out of eight games. Teams A and B play in the championship, but team A has a 60% chance of winning compared to team B.

a.Find the probability that team A wins the championship

b.What is the probability that team A wins in 7 games.

c.If there’s a playoff series in which the winner emerges by winning 2 out of 3 games, what is the probability that team A wins the series.

Suppose x has a normal distribution with mean μ = 32 and standard deviation σ = 12. Describe the distribution of x values for sample size n = 4. (Round σx to two decimal places.) μx = Incorrect: Your answer is incorrect. σx = Describe the distribution of x values for sample size n = 16. (Round σx to two decimal places.) μx = σx = Describe the distribution of x values for sample size n = 100. (Round σx to two decimal places.) μx = σx = How do the x distributions compare for the various samples sizes? The means are the same, but the standard deviations are increasing with increasing sample size. The standard deviations are the same, but the means are increasing with increasing sample size. The standard deviations are the same, but the means are decreasing with increasing sample size. The means and standard deviations are the same regardless of sample size. The means are the same, but the standard deviations are decreasing with increasing sample size.

What is a strategy for handling a confounder?

a) None of the above

b) Enroll all patients and stratify the data

c) All of the above

d) Enroll only patients that report no exposure to the confounder

e) Enroll only patients that report exposure to the confounder