The researcher from problem 1 has a graduate student who is exploring doing his master's degree in the area of community-based mental health services. The student wants to assess whether the public health agencies in the southern part of the state have fewer resources than the agencies in the northern part of the state. He obtained survey data from a convenience sample of 12 agencies, 6 from the northern region and 6 from the southern region. The survey items used this response scale about their funding: 3 = more than enough funding, 2 = about enough funding, 1 = not enough funding (the survey did not interval level data). Here are the data:

Northern: 3, 3, 2, 1, 3, 2

Southern: 2, 1, 3, 2, 1, 2

A machine produces coins such that the probability of heads, p, follows a Beta distribution with parameters (α, β) = (1, 1). A coin produced by this machine is picked at random and tossed independently n times. Let Y be the number of heads.

1. (a) Find E[Y ].

2. (b) Write down the pmf for Y (your answer can include unevaluated integrals and

   combination numbers [aka “n choose m” symbols]).

Question 3:

Suppose that 1000 customers are surveyed and 850 are satisfied or very satisfied with a corporation’s products and services.

1. Test the hypothesis H₀: p = 0.9 against H₁: p ≠ 0.9 at α = 0.05. Find the p-value.
2. Explain how the question in part (a) could be answered by constructing a 95% two-sided confidence interval for p.

W71) I am study Excel Functions. Please answer in detail using Excel functions.

Parking Tickets – The Chicago police department claims that it issues an average of only 60 parking tickets per day. The data below, reproduced in your Excel answer workbook, show the number of parking tickets issued each day for a randomly selected period of 30 days. Assume σ =13.42.   State the null and alternate hypotheses, as well as the claim, which (hint!) is in the null hypothesis. Is there enough evidence to reject the group’s claim at α = .05?   (As with all of these exercises, use the P-value method, rounding to 4 digits.) (Hint: so since we know the population standard deviation, use the standard normal distribution z-test .) (Monday class)

              79         78         71         72         69         71              57         60

              83         36         60         74         58         86              48         59

              70         66         64         68         52         67              67

              68         73         59         83         85         34              73

We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different “digits” {0,1,…,9}.{0,1,…,9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0,1,…,9,A,B,C,D,E,F}.{0,1,…,9,A,B,C,D,E,F}. So for example, a 3 digit hexadecimal number might be 2B8.

How many 3-digit hexadecimals are there in which the first digit is E or F?

How many 4-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)?

How many 4-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)?

In a recent survey, 43 students reported whether they liked their potatoes Mashed, French-fried, or Twice-baked. 24 liked them mashed, 23 liked French fries, and 12 liked twice baked potatoes. Additionally, 11 students liked both mashed and fried potatoes, 9 liked French fries and twice baked potatoes, 10 liked mashed and baked, and 2 liked all three styles. How many students hate potatoes? Explain why your answer is correct.

How many positive integers less than 975 are multiples of 8, 7, or 9? Use the Principle of Inclusion/Exclusion.

We want to build 5 letter “words” using only the first n=12n=12 letters of the alphabet. For example, if n=5n=5 we can use the first 5 letters, {a,b,c,d,e}{a,b,c,d,e} (Recall, words are just strings of letters, not necessarily actual English words.)

1. How many of these words are there total?
2. How many of these words contain no repeated letters?
3. How many of these words start with the sub-word “ade”?
4. How many of these words either start with “ade” or end with “be” or both?
5. How many of the words containing no repeats also do not contain the sub-word “bed”?

1. If all the letters of the word ABOUT are arranged at random in a line, find the probability that the arrangement will begin with AB...

2.   

The odds of throwing two fours on a single toss of a pair of dice is 1:35
What is the probability of not throwing two fours? (Hint: there are 2 conversions here)

All answers are written as fractions for consistency....

Select one:

a. 35/36

b. 1/36

c. 1/35

d. 35/1

Discuss the real–world applications where probabilities are used. (Ex. Stock market trading; Medical treatment plans; etc.)

The null hypothesis plays an important role in significance testing. Explain the concept underlying the null hypothesis and the role it plays in tests of statistical significance (hint: think of the logic involved in the decision making process).

The weights of ice cream cartons are normally distributed with a mean weight of 13 ounces and a standard deviation of 0.6 ounce. ​(a) What is the probability that a randomly selected carton has a weight greater than 13.19 ​ounces? ​(b) A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 13.19 ​ounces?

Please make detailed answers to the problem. So I can understand fully.

Thank you

Question 6:

A market gardener is planning a planting scheme for the new growing season, and there are 12 different crops to choose from – 8 of which are vegetables and 4 of which are grains.

1. a) Calculate the number of different ways he can select 7 crops to plant, if there are no restrictions.
2. b) Redo (a), with the extra restriction that he must select at most 2 grain crops.
3. c) Say that he has selected the following 7 crops: tomatoes, carrots, peas, radishes, beans, lettuce, cilantro. He wishes to plant these in 7 adjacent rows, with 1 crop in each row. Calculate the number of different ways he can arrange these rows, if there are no other restrictions.
4. d) Redo (c), with the extra restriction that the tomatoes and carrots must be planted in adjacent rows.
5. e) Redo (d), with the further extra restriction that the peas and beans must not be planted in adjacent rows.
6. f) Redo (e), with the further extra restriction that the 7 crops must be planted in a circle, instead of in adjacent rows.

1.A particular bank requires a credit score of 640 to get approved for a loan. After taking a sample of 107 customers, the bank finds the 95% confidence interval for the mean credit score is:

662 < μ < 739

Can we be reasonably sure that a majority of people will have a credit score over 640 and be able to get the loan?

• Yes
• No

Why or why not?

2. If n=27, x¯(x-bar)=31, and s=12, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

1. Say 5% of circuit boards tested by a manufacturer are defective. Let Y be the number of defective boards in a random sample of size n = 25.

   1. What kind of random variable is Y ? In particular, write Y ~Distribution(p, n), where you fill in the correct distribution name and parameters p and n.

   2. Determine P (Y ≥ 5).

   3. DetermineP(1≤Y ≤4).

   4. What is the probability that none of the 25 boards are defective?

1. Rejecting the null hypothesis that the population slope is equal to zero or no relationship and concluding that the relationship between x and y is significant does not enable one to conclude that a cause-and-effect relationship is present between x and y. Explain why.

2. Discuss the statistics that must be evaluated when reviewing the regression analysis output. Provide examples of what the values represent and an explanation of why they are important.

Random samples of size n = 330 are taken from a population with p = 0.09.

a. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p⎯⎯p¯ chart. (Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.)

Centerline _________

Upper control limit __________

Lower control limit __________

b. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p⎯⎯p¯ chart if samples of 210 are used. (Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.)

Centerline_____________

Upper control limit____________

Lower control limit____________

c. Discuss the effect of the sample size on the control limits. (fill in the blanks)

The control limits have a __________ spread with smaller sample sizes due to the _____________ standard error for the smaller sample size.

Textbook publishers must estimate the sales of new​ (first-edition) books. The records indicate that 25​% of all new books sell more than​ projected, 30​% sell close to the number​ projected, and 45​% sell less than projected. Of those that sell more than​ projected, 55​% are revised for a second​ edition, as are 40​% of those that sell close to the number​ projected, and 25​% of those that sell less than projected.

a. What percentage of books published go to a second​ edition?