Compute the confidence interval for the difference of two population means. Show your work.

Sample Mean 1= 17

Population standard deviation 1= 15

n1= 144

Sample Mean 2= 26

Population Standard Deviation 2= 13

n2 = 121

Confidence Level= 99

The variance in drug weights is critical in the pharmaceutical industry. For a specific drug, with weights measured in grams, a sample of 20 units provided a sample variance of s^2 = 0.49.

a)  construct a 90% confidence interval estimate for the population variance

b) construct a 90% confidence interval estimate of the population standard deviation

Find the​ t-value such that the area in the right tail is 0.025 with 9 degrees of freedom. nothing ​(Round to three decimal places as​ needed.) ​(b) Find the​ t-value such that the area in the right tail is 0.25 with 29 degrees of freedom. nothing ​(Round to three decimal places as​ needed.) ​(c) Find the​ t-value such that the area left of the​ t-value is 0.15 with 7 degrees of freedom.​ [Hint: Use​ symmetry.] nothing ​(Round to three decimal places as​ needed.) ​(d) Find the critical​ t-value that corresponds to 60​% confidence. Assume 13 degrees of freedom. nothing ​(Round to three decimal places as​ needed.)

1. Utilizing the sample size chart, what would be the minimum sample size for the following situations?

a. one sample test              ES = .8,*a = .05/2, 1- B = .90

b. two sample test (independent)   ES = .8, *a = .01, 1- B = .80

c. two sample test (independent)    ES = .2, *a = .05/2, 1- B = .95

d. one sample test      ES = .5, *a = .01, 1- B = .80

e. two sample test       ES = .8, *a = .05/2, 1- B = .95

f. one sample test        ES = .5, *a = .01, 1- B = .90

The eigenvalue is a measure of how much of the variance of the observed variables a factor explains. Any factor with an eigenvalue ≥1 explains more variance than a single observed variable, so if the factor for socioeconomic status had an eigenvalue of 2.3 it would explain as much variance as 2.3 of the three variables. This factor, which captures most of the variance in those three variables, could then be used in another analysis. The factors that explain the least amount of variance are generally discarded. How do we determine how many factors are useful to retain?

Consider the following results for two independent random samples taken from two populations.

Sample 1:

n1 = 40

x̅1 = 13.9

σ1 = 2.3

Sample 2:

n2 = 30

x̅2 = 11.1

σ2 = 3.4

What is the point estimate of the difference between the two population means? (to 1 decimal)

Provide a 90% confidence interval for the difference between the two population means (to 2 decimals).

Provide a 95% confidence interval for the difference between the two population means (to 2 decimals).

Last rating period, the percentages of viewers watching several channels between 11 P.M. and 11:30 P.M. in a major TV market were as follows: WDUX (News) WWTY (News) WACO (Cheers Reruns) WTJW (News) Others 15% 21% 25% 17% 22% Suppose that in the current rating period, a survey of 2,000 viewers gives the following frequencies: WDUX (News) WWTY (News) WACO (Cheers Reruns) WTJW (News) Others 280 401 504 354 461

(a) Show that it is appropriate to carry out a chi-square test using these data. Each expected value is ≥

(b) Test to determine whether the viewing shares in the current rating period differ from those in the last rating period at the .10 level of significance. (Round your answer to 3 decimal places.) χ2 χ 2 H0. Conclude viewing shares of the current rating period from those of the last.

The weight of trout in a fish farm follows the distribution N(200,502). A trout is randomly selected. (a) What is the probability that its weight does not exceed 175g? (b) What is the probability that its weight is greater than 230g? (c) What is the probability that its weight is between 225g and 275g? (d) What is the probability that out of eight trout selected randomly from the fish farm, less than three of them will not weigh more than 175g?

1. At a particular amusement park, most of the live characters have height requirements of a minimum of 57 in. and a maximum of 63 in. A survey found that​ women's heights are normally distributed with a mean of 62.4 in. and a standard deviation of 3.6 in. The survey also found that​ men's heights are normally distributed with a mean of 68.3 in. and a standard deviation of 3.6 in.
   
   Part 1:
   Find the percentage of men meeting the height requirement.
   
   The percentage of men who meet the height requirement is ____?____.
   ​(Round answer to nearest hundredth of a percent - i.e. 23.34%)
   
   What does the result suggest about the genders of the people who are employed as characters at the amusement​ park?
   Since most men___?___ the height​ requirement, it likely that most of the characters are ___?___ .
   (Use "meet" or "do not meet" for the first blank and "men" or "women" for the second blank.)
   
   Part 2: I was able to solve part 2 on my own.
   If the height requirements are changed to exclude only the tallest​ 50% of men and the shortest​ 5% of​ men, what are the new height​ requirements?
   The new height requirements are a minimum of 62.4 in. and a maximum of 68.3 in.
   ​(Round to one decimal place as​ needed.)

GRADED PROBLEM SET #5

Answer each of the following questions completely. There are a total of 20 points possible in the assignment.

1. (8 pts) Based on past results found in the Information Please Almanac there is a 0.1919 probability that a baseball World Series will last four games, a 0.2121 probability that it will last five games, a 0.2223 probability that it will last six games, and a 0.3737 probability that it will last seven games.
   1. Does the given information describe a probability distribution? Explain.

2. Assuming that the given information describes a probability distribution, find the mean and standard deviation for the number of games in World Series.

2. (4 pts) Men heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. Doorframes have to be designed so that 99.9% of all men can pass under without stooping. What is the height of the doorframe?

3. (8 pts) Tree diameters in a plot of land are normally distributed with a mean of 14 inches and a standard deviation of 3.2 inches.
   1. What is the probability that an individual tree has a diameter between 13 inches and 16.3 inches?

2. What is the probability that an individual tree has a diameter less than 12 inches?

3. What is the probability that an individual tree has a diameter of at least 15 inches?

4. Find the cutoff for the 80^th percentile of tree diameters. (Provide the probability notation)

Part 1: Analyzing your College’s School Graduation Rate

You recently went through your college website and some information there got your attention. There was a claim that your college has a 77% graduation rate. You thought it would be interesting to check the validity of this statement since these days you are reading about hypothesis testing in your Statistics online course. You contacted the research department and got access to the data for the last graduation and out of 200 students 165 graduated.

To complete Case 1 please answer the following questions:

1. If you are to conduct a hypothesis test using the data above,
   1. Which test (t-test or z test) would you think be appropriate and why?

2. Is this should be a test on population proportion or mean?

3. Calculate the sample statistics (sample mean or sample proportion based on the information given) (1 mark)

2. Conduct the hypothesis test with a 0.01 level of significance. You may use ‘the percentage of graduates not equals to 0.77’ as your alternative hypothesis. Please show your work, the 5 steps as described in the textbook.

3. Construct a 95% confidence interval for the population proportion of graduates. Show your work.

The probability that a random gift box in Overwatch (PC game) has one of the character skins you want is .1. Suppose you get a gift box every game you play, and that you play until you have obtained 2 of these skins. a. What is the probability that you play until you have x boxes that do not have the desired prize? Write down the formula as well as the notation for the pdf. b. What is the probability that you play exactly 5 times? Show the R code. c. What is the probability that you play at most 5 times? Show the R code. d. How many boxes without the desired skins do you expect to get? Show the formula

Describe the sampling distribution of ModifyingAbove p with caret. Assume the size of the population is 15 comma 000. nequals200​, pequals0.4 Choose the phrase that best describes the shape of the sampling distribution of ModifyingAbove p with caret below. A. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10. B. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10. C. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10. D. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10. Determine the mean of the sampling distribution of ModifyingAbove p with caret. mu Subscript ModifyingAbove p with caret Baseline equals nothing ​(Round to one decimal place as​ needed.) Determine the standard deviation of the sampling distribution of ModifyingAbove p with caret. sigma Subscript ModifyingAbove p with caret Baseline equals nothing ​(Round to three decimal places as​ needed.)

a.) Suppose that government data show that 8% of adults are full‑time college students and that 30% of adults are age 55 or older. Complete the passage describing the relationship between the two aforementioned events. Although (0.08)⋅(0.30)=0.024, we cannot conclude that 2.4% of adults are college students 55 or older because the two events __________(are/are not) ________(independent/disjoint)

b.) In New York State's Quick Draw lottery, players choose between one and ten numbers that range from 11 to 80.80. A total of 2020winning numbers are randomly selected and displayed on a screen. If you choose a single number, your probability of selecting a winning number is 2080,2080, or 0.25.0.25. Suppose Lester plays the Quick Draw lottery 66 times. Each time, Lester only chooses a single number.

What is the probability that he loses all 66 of his lottery games? Please give your answer to three decimal places.

c.) Consider the sample space of all people living in the United States, and within that sample space, the following two events.

??=people who play tennis=people who are left‑handedA=people who play tennisB=people who are left‑handed

Suppose the following statements describe probabilities regarding these two events. Which of the statements describe conditional probabilities? Select all that apply:

-Two‑tenths of a percent of people living in the United States are left‑handed tennis players.

-Two percent of left‑handed people play tennis.

-Of people living in the United States, 3.7% play tennis.

-There is a 10.2% chance that a randomly chosen person is left‑handed.

-The probability is 5.4% that a tennis player is left‑handed.

-There is a 13.7% probability that a person is a tennis player or left‑handed.

d.)

Of all college degrees awarded in the United States, 50%50% are bachelor's degrees, 59%59% are earned by women, and 29%29% are bachelor's degrees earned by women. Let ?(?)P(B) represent the probability that a randomly selected college degree is a bachelor's degree, and let ?(?)P(W) represent the probability that a randomly selected college degree was earned by a woman.

What is the conditional probability that a degree is earned by a woman, given that the degree is a bachelor's degree? Please round your answer to the two decimal places.

The Bogard Corporation produces three types of bookcases, which it sells to large office supply companies. The production of each bookcase requires two machine operations, trimming and shaping, followed by assembly, which includes inspection and packaging. Each type requires 0.4 hours of assembly time, but the machining operations have different processing times, as shown in the table below (in hours per unit). Each machine is available for 150 hours per month, and the current size of the assembly department provides capacity of 200 hours. Each bookcase produced yields a unit profit contribution as shown below.

Standard Narrow Wide

Trimmer 0.2 0.4 0.6

Shaper 0.6 0.2 0.5

Profit $8 $6 $10

Write a linear optimization model (i.e., identify decision variables, objective function and constraints)