In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 536 said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12.

(a) Test, at 5% significance level, if this sample provides evidence that the proportion of Americans who are dissatisfied with education in kindergarten through grade 12 differs significantly from 50%. (Be sure to state all the 5 steps involved in a hypothesis testing, Hypothesis, Observed statistic, p-value, decision and conclusion in contest of the problem) Hint: Use Statkey to get your p-value.

(b) Is the Test Significant? Why or Why not.

A casino introduces a new game. In this game you roll a die and the upper most number is recorded. If you roll an odd you lose. If you roll a 2 you win $1, if you roll a 4 you win $5 and if you roll a 6 you win $10.

A) If the game costs $5 to play what is the expected gain/loss of the game?

B) Instead of $5 to play, what should the cost to play be to make this a fair game?

Each student arrives in office hours one by one, independently of each other, at a steady rate. On average, three students come to a two-hour office hour time block. Let S be the number of students to arrive in a two-hour office hour time block.

What is the distribution of S? What is its parameter?

Group of answer choices

S ∼ Geo(1/3)

S∼Pois(3)

S∼Bin(2,1/3)

S-Pois(1.5)

What is the probability that S = 4?

What is the probability that S ≤ 2?

What is the variance of S?

What is the expected value of S?

A survey of 2,000 American citizens was taken in 2016. The results show that 1,000 people owned a rifle, 800 owned a hand gun, 750 owned a shot gun, 250 owned a hand gun and a rifle, 100 owned a rifle and a shot gun, 300 owned a hand gun and a shot gun and 50 owned all three.

A) Draw a Venn Diagram of this information

B) How many people only own a hand gun or only own a rifle?

C) How many people don’t own a gun at all?

sxplain controllable factors and their types in doe with detail and example with subpart also

write full answer and not copy of google otherwise dislike

1) A book manufacturing company has two different production plants, plant A and plant B. 40% of books come from plant A. Of the books that come from plant A 30% are defective and 70% work as intended. Of the books from plant B 10% are defective and 90% work as intended. On top of this 10% of the defective books from plant A explode.

A) Draw a tree diagram of this data.

B) What is the probability of randomly selecting

C) What is the probability of randomly selecting adefective book which doesn’t explode?

I. Consider the random experiment of rolling a pair of dice. Note: Write ALL probabilities as reduced fractions or whole numbers (no decimals).

2) How many outcomes does the sample space contain? _____36________

3)Draw a circle (or shape) around each of the following events (like you would circle a word in a word search puzzle). Label each event in the sample space with the corresponding letter.

A: Roll a sum of 3.

B: Roll a sum of 6.

C: Roll a sum of at least 9.

D: Roll doubles.

E: Roll snake eyes (two 1’s). F: The first die is a 2.

3) Two events are mutually exclusive if they have no outcomes in common, so they cannot both occur at the same time.

Are C and F mutually exclusive? ___________

Using the sample space method (not a special rule), find the probability of rolling a sum of at least 9 and rolling a 2 on the first die on the same roll. P(C and F) = __________

Using the sample space method (not a special rule), find the probability of rolling a sum of at least 9 or rolling a 2 on the first die on the same roll.

P(C or F) = __________

4) Special case of Addition Rule: If A and B are mutually exclusive events, then

P(A or B) = P(A) + P(B)

Use this rule and your answers from page 1 to verify your last answer in #6:

P(C or F) = P(C) + P(F) = ________ + ________ = _________

5) Are D and F mutually exclusive? __________

Using the sample space method, P(D or F) = _________

6) Using the sample space method, find the probability of rolling doubles and rolling a “2” on the first die.

P (D and F) = _______

7) General case of Addition Rule: P(A or B) = P(A) + P(B) – P(A and B)

Use this rule and your answers from page 1 and #9 to verify your last answer in #8:

P(D or F) = P(D) + P(F) – P(D and F) = ________ + ________ − ________ = _________

8) Two events are independent if the occurrence of one does not influence the probability of the other occurring. In other words, A and B are independent if P(A|B) = P(A) or if P(B|A) = P(B).

Compare P(D|C) to P(D), using your answers from page 1: P(D|C) = ________ P(D) = ________ Are D and C independent? _________ because _______________________________

When a gambler rolls at least 9, is she more or less likely to roll doubles than usual? ___________ Compare P(D|F) to P(D), using your answers from page 1: P(D|F) = ________ P(D) = ________

Are D and F independent? __________ because ______________________________

9) Special case of Multiplication Rule: If A and B are independent, then P(A and B) = P(A) · P(B).

Use this rule and your answers from page 1 to verify your answer to #9: P(D and F) = P(D) • P(F) = ________ · ________ = ________ .

10) Find the probability of rolling a sum of at least 9 and getting doubles, using the sample space method.

P(C and D) = ___________ .

11) General case of Multiplication Rule: P(A and B) = P(A) · P(B|A).

Use this rule and your answers from page 1 to verify your answer to #13: P(C and D) = P(C) • P(D|C) = ________ · ________ = ________ .

1. Researchers conducted a study looking at the effects of cooking container type (aluminum, clay, iron) and food type (meat, legumes, vegetables) on the amount of iron present in the food after cooking. They cooked the same weight of each of the 3 food types for a similar amount of time in each of the cooking container types and replicated each. See columns “type”, “food” and “iron” on the ANOVA_2Way_data file. Does iron content vary by food type and container type after the food has been cooked?

1. What are the null and alternate hypotheses?

2. Check the assumption of normality of the response with a histogram

3. Run the 2-Way ANOVA (including the interaction) and interpret the Sums of Squares, Mean Squares, F statistics, and P values

4. Make an appropriate interaction plot

5. Interpret the results and determine if you accept or reject the null hypotheses

   type	food	iron
   Aluminum	meat	1.77
   Aluminum	meat	2.36
   Aluminum	meat	1.96
   Aluminum	meat	2.14
   Clay	meat	2.27
   Clay	meat	1.28
   Clay	meat	2.48
   Clay	meat	2.68
   Iron	meat	5.27
   Iron	meat	5.17
   Iron	meat	4.06
   Iron	meat	4.22
   Aluminum	legumes	2.4
   Aluminum	legumes	2.17
   Aluminum	legumes	2.41
   Aluminum	legumes	2.34
   Clay	legumes	2.41
   Clay	legumes	2.43
   Clay	legumes	2.57
   Clay	legumes	2.48
   Iron	legumes	3.69
   Iron	legumes	3.43
   Iron	legumes	3.84
   Iron	legumes	3.72
   Aluminum	vegetables	1.03
   Aluminum	vegetables	1.53
   Aluminum	vegetables	1.07
   Aluminum	vegetables	1.3
   Clay	vegetables	1.55
   Clay	vegetables	0.79
   Clay	vegetables	1.68
   Clay	vegetables	1.82
   Iron	vegetables	2.45
   Iron	vegetables	2.99
   Iron	vegetables	2.8
   Iron	vegetables	2.92

A study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below.

1. Find the correlation coefficient: r=r=    Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are:
   H0:H0: ? μ ρ r  == 0
   H1:H1: ? ρ μ r   ≠≠ 0
   The p-value is:      Round to 4 decimal places.
   
   
   
   
   
3. Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
   • There is statistically significant evidence to conclude that a person who watches more movies will read fewer books than a person who watches fewer movies.
   • There is statistically significant evidence to conclude that a person who watches fewer movies will read fewer books than a person who watches fewer movies.
   • There is statistically insignificant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the use of the regression line is not appropriate.
   • There is statistically significant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the regression line is useful.
4. r2r2 =  (Round to two decimal places)
5. Interpret r2r2 :
   • There is a large variation in the number books people read each year, but if you only look at people who watch a fixed number of movies each year, this variation on average is reduced by 62%.
   • Given any fixed number of movies watched per year, 62% of the population reads the predicted number of books per year.
   • There is a 62% chance that the regression line will be a good predictor for the number of books people read based on the number of movies they watch each year.
   • 62% of all people watch about the same number of movies as they read books each year.
6. The equation of the linear regression line is:   
   ˆyy^ =   + xx    (Please show your answers to two decimal places)
   
   
   
   
   
7. Use the model to predict the number of books read per year for someone who watches 2 movies per year.
   Books per year =  (Please round your answer to the nearest whole number.)
   
   
   
   
   
8. Interpret the slope of the regression line in the context of the question:
   • For every additional movie that people watch each year, there tends to be an average decrease of 0.76 books read.
   • As x goes up, y goes down.
   • The slope has no practical meaning since people cannot read a negative number of books.
   
   
   
   
   
   
9. Interpret the y-intercept in the context of the question:
   • The average number of books read per year is predicted to be 5 books.
   • The best prediction for a person who doesn't watch any movies is that they will read 5 books each year.
   • The y-intercept has no practical meaning for this study.
   • If someone watches 0 movies per year, then that person will read 5 books this year.

There are two servers. Hiba has just started service at server 1, while Daniella has just started service at server 2. Hiba’s service time at server 1 is exponentially distributed with mean 1/4 hour. Daniella’s service time at server 2 is exponentially distributed with mean 1/6 hour. Daniella’s service time and Hiba’s service time are independent.

(a) What is the probability that Hiba finishes service before Daniella?

(b) What is the expected time in minutes until the first person finishes?

(c) What is the expected time in minutes until the second person finishes

QUESTION 4 ( 8 marks)

A telemarketer is able make a sale on 27% of the phone calls he makes. Assume that he makes 12 calls in an hour. Answer the following questions, assuming a binomial probability distribution:

Required:

1. What is the probability that he will make exactly four sales in the course of an hour? ( 3 marks)
2. What is the probability that he will make at least three sales in the course of an hour? Hint: Use the approach that requires the least calculation work! ( 5 marks)

Suppose 1.6% of the antennas on new Nokia cell phones are defective. For a random sample of 235 antennas, answer the following questions (assume a Poisson probability distribution):

Required:

1. Calculate the mean and standard deviation for the probability distribution of the number of defective antennas in the random sample. ( 2 marks)
2. What is the probability that exactly five of the antennas will be defective? What is the probability that less than three antennas will be defective? ( 4 marks)

i need fully explanation and calculation of the answer

QUESTION 2  

According to Michael Theatre Ltd., the mean cost to run a nightly theatre performance is $3,200 with a standard deviation of $460. Performance costs are known to follow a normal probability distribution.

Required:

1. What percentage of the performances will cost less than $2,850 to run? Sketch a normal curve and shade the desired area on your diagram. ( 4 marks)
2. What percentage of the performances will cost between $3,250 and $3,520 to run? Sketch a normal curve and shade the desired area of your diagram. ( 4 marks)
3. What percentage of the performances will cost between $2,300 and $3,520 to run? Sketch a normal curve and shade the desired area on your diagram. ( 4 marks)
4. What percentage of the performances will cost less than $3,750 to run? Sketch a normal curve and shade the desired area of your diagram. Also, Six percent (6 %) of all shows will cost less than what dollar amount? Sketch a normal curve and shade the desired area of your diagram. ( 8 marks)

I Need the full calculation and explanation of the answers.

QUESTION 1

Studd Enterprises sells big-screen televisions. A concern of management is the number of televisions sold each day. A recent study revealed the number of days that a given number of televisions were sold.

# of TV units sold      # of days

0                             2

1.                         4

2.                       18

3.                       12

4.                       10

5.                         4

Answer the questions below. For each part, show your calculations and/or explain briefly how you arrived at your answer, as appropriate or needed.

Required:

1. Convert the frequency distribution above into a probability distribution (or relative frequency distribution) showing the proportion of days (rather than the number of days) that the number of televisions sold was 0, 1, 2, 3, 4, and 5 respectively. ( 3 marks)
2. Compute the mean of this general discrete probability distribution. ( 3 marks)
3. Compute the standard deviation of this general discrete probability distribution. ( 5 marks)
4. What is the probability that exactly 4 televisions will be sold on any given day? What is the probability that 2 or more televisions will be sold on any given day? What is the probability that less than 2 televisions will be sold on any given day? What is the probability that between 1 and 4 televisions inclusive will be sold on any given day? (4 mark)

I need the full Explanation and calculation of the answer