Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The survey data was collected via random-digit-dial telephone interviews conducted July 1-12, 2019 with a random sample of 1525 adults living in all 50 U.S. states with a minimum quota of 70% cellphone respondents and 30% landline respondents, with additional minimum quotas by time zone within region. The following table summarizes their results for men and women: Men Women Total Vape 92 31 123 Do Not Vape 924 478 1402 Total 1016 509 1525 Problem 2. Does the data suggest that a greater proportion of men vape compared to women? Conduct a hypothesis test to at the 5% significance level by completing the following steps: State the null and alternative hypotheses. Be sure to include proper statistical notation. Check the conditions for inference. Compute the test statistic. For full credit, be sure to show your work. Determine the p-value or the critical value (depending on the method you prefer). Either way, be sure to show your work by drawing a sketch. Using either the p-value or critical value method, make a decision about the null hypothesis. Be sure to show how your decision was made. Based on the results of the hypothesis test, does it appear that “use of e-cigarettes” and “gender” are independent variables? In other words, is it equally likely for a man to vape as it is for a woman to vape? Explain. Would the results of the hypothesis test change at the 1% significance level? Explain.

A hand of 13 cards is dealt from a standard deck of 52 playing cards. What is the probability that it contains more spades (♠) than hearts (♡) given that the hand contains at least two spades?

A cola-dispensing machine is set to dispense 8 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manufacturer of the machine would like to set the control limit in such a way that, for samples of 34, 5% of the sample means will be greater than the upper control limit, and 5% of the sample means will be less than the lower control limit.

1. At what value should the control limit be set? (Round z values to two decimal places. Round your answers to 2 decimal places.)
2. If the population mean shifts to 7.6, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
3. If the population mean shifts to 8.7, what is the probability that the change will not be detected? (Round your intermediate calculations to 2 decimal places and final answer to 4 decimal places.)

Applications of Statistical Process Control and Quality Improvement Tools in Transactional and

Service Business.

The tools are:

1. Cause and Effect Analysis.

2. Check sheets/ tally sheets.

3. Graphs.

4. Histograms.

5. Pareto analysis.

6. Scatter analysis.

7. Control charts.

. For discussion, I want you to discuss how these tools are being used in your realm of work? If they are not

being used, then how do you see them being used? Identify at least one tool being used and explain

how it is being used in your realm of work, and identify at least one tool that is not being used and how

it may be used to benefit your job.

(Note: The answer has to be typed, not hand written nor a picture.) Thank you.

A research group conducted an extensive survey of 3144 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question, "What does success mean to you?" 1508 responded, "Personal satisfaction from doing a good job." Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. Find a 90% confidence interval for p. (Round your answers to three decimal places.)

The data below are from a study conducted by a consumer research group on the fuel efficiency (rated based on city miles per gallon) of the 30 top-selling U.S. automobiles.

23 20 16 13 34 27

24 10 16 12 34 26

14 31 15 12 16 36

18 22 15 19 28 38

10 16 14 23 19 44

1. Enter the data into a spreadsheet. Be sure to clearly label and neatly format your spreadsheet.

2. Calculate the sum of these data two different ways: a. By writing your own formula. Clearly label the result. b. By using the SUM spreadsheet function. Clearly label the result

. 3. Use the COUNT function to calculate the N of this sample data set. Clearly label the result.

4. Calculate the arithmetic average (mean) of these data by writing your own formula. Clearly label.

5. Create a new column of data in which you subtract the mean fuel efficiency from each individual fuel efficiency score (i.e., MPG – mean). Be sure to use the proper relative and absolute references (indicated with $ signs) to perform these calculations.

6. Now compute the sum, N, and mean of your new (MPG – mean) scores.

7. Create one more new column of data in which you square each of the (MPG – mean) scores. 8. Finally, compute the sum, N, and mean of your new (MPG – mean)^2 scores

A group of 1000 students wrote an entrance exam for the University of Statistics. The mean score was 62 with a standard deviation of 12. Assuming a Normal Distribution, answer the following questions:

1. What is the probability of a student scoring above 75?
2. What is the probability of a student failing? (i.e. below 50) How many students failed?
3. What is the minimum mark you would need to score to be in the top 10%?
4. What is the minimum mark you would need to score to be in the top 1%?
5. How many people scored below 30?
6. What is the probability of scoring between 60 and 80?

In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 1.9​% with a standard deviation of 6.3​%. Consider the Normal model ​N(0.019​,0.063​) for the returns of these mutual funds. ​
a) What value represents the 40th percentile of these​ returns? ​
b) What value represents the 99th​ percentile?
​c) What's the​ IQR, or interquartile​ range, of the quarterly returns for this group of​ funds?

Must show all needed steps in getting to your final answer. And, express your final answer as a decimal.

Show every step NEATLY please

NEATLY AND VERY CLEAR AND READABLE

PLEASE TYPE ANSWER AND WORK

NEATLY AND VERY CLEAR AND READABLE

PLEASE TYPE ANSWER AND WORK

Part 1) Suppose that you are planning to travel a certain air route via plane once each week for your new job. Also, assume that there is a 3% chance that your outbound flight may be cancelled on any given week due to various issues. How many consecutive outbound weekly flights can you fly before the probability of another successful flight (that is, a flight that is not cancelled) drops to 50% or less?

Part 2) Assume that you are playing a game in which you pull a lever and a light comes on. The light will be either red or green. Assume that on any given pull of the lever, P(Red Light) = .40 and P(Green Light) = .60. Find the probability that in pulling the lever 5 times that you will get your 3rd Green Light on the 5th pull of the lever.

Part 3) Suppose in front of you are three boxes that look identical. Further, you are told that one box contains two $1 bills, one contains two $100 bills, and one contains one $1 bill and one $100 bill. You are permitted to choose one box. Then you are asked to remove one bill from the box you chose without looking at the other bill in that box. Suppose that a $100 bill comes out. What is the probability that the other bill in that box is $100?

A 2007 Carnegie Mellon University study reported that online shoppers were willing to pay, on average, more than an extra $0.60 on a $15 purchase in order to have better online privacy protection.
A sample of ?=22n=22 online shoppers was taken, and each was asked how much extra would you pay, on a $15 purchase, for better online privacy protection?'' The data is given below, in $'s.

0.79,0.41,0.67,0.67,0.83,0.76,0.55,0.92,0.61,0.57,0.54,1.25,0.70,0.85,0.59,0.59,0.90,0.67,0.62,0.67,0.44,0.500.79,0.41,0.67,0.67,0.83,0.76,0.55,0.92,0.61,0.57,0.54,1.25,0.70,0.85,0.59,0.59,0.90,0.67,0.62,0.67,0.44,0.50

(a) Do the data follow an approximately Normal distribution? Use alpha = 0.05.   ? yes no  

(b) Determine the ?P-value for this Normality test, to three decimal places.
?=P=

equation editor

Equation Editor

(c) Choose the correct statistical hypotheses.
A. ?0:?>0.60??:?=0.60H0:μ>0.60HA:μ=0.60
B. ?0:?⎯⎯⎯⎯⎯=0.60,??:?⎯⎯⎯⎯⎯<0.60H0:X¯=0.60,HA:X¯<0.60
C. ?0:?>0.60,??:?<0.60H0:μ>0.60,HA:μ<0.60
D. ?0:?⎯⎯⎯⎯⎯=0.60,??:?⎯⎯⎯⎯⎯>0.60H0:X¯=0.60,HA:X¯>0.60
E. ?0:?=0.60,??:?≠0.60H0:μ=0.60,HA:μ≠0.60
F. ?0:?=0.60??:?>0.60H0:μ=0.60HA:μ>0.60


(d) Determine the value of the test statistic for this test, using two decimals in your answer.
Test Statistic =

equation editor

Equation Editor

(e) Determine the ?P-value for this test, enter your answer to three decimals.
?=P=

equation editor

Equation Editor

(f) Based on the above calculations, we should  ? reject not reject  the null hypothesis. Use alpha = 0.05

Describe 2 (two) methods that will be useful in enhancing data quality?

Would internal validity and reliability be correct for this question or would you recommend something else?

ANSWER USING R CODE

Using the dataset 'LakeHuron' which is a built in R dataset describing the level in feet of Lake Huron from 1872- 1972. To assign the values into an ordinary vector,x, we can do the following 'x <- as.vector(LakeHuron)'. From there, we can access the data easily. Assume the values in X are a random sample from a normal population with distribution X. Also assume the X has an unknown mean and unknown standard deviation. With this information in mind, answer the following.

a) The sample mean of x

b) the sample mean of 8X

c) Using this data, create a 97% confidence interval for X using the a t-distribution critical value tstar.

d) Using this data, create a 3 percent level test of H0:mu = 578.9 versus the alternative Ha:mu > 578.9. USing tis information, calculate the value of the z-statistic

e) With the z-statistic, calculate the appropriate p-value.

What is the Central Limit Theorem? Discuss an example of its application.

1) A survey was conducted that asked 1002 people how many books they had read in the past year. Results indicated that x=12.9 books and s=16.6 books. Construct a 99​% confidence interval for the mean number of books people read. Interpret the interval.

Was there discrimination on the Titanic? Were first-class passengers given greater
access to life boats?
The unsinkable liner Titanic collided with an iceberg on her maiden voyage
in 1912 and sank with great loss of life. On board were 1317 passengers, some of
whom had paid a very much higher fare than others for the voyage. A not very
subtle sub-text in the most recent Titanic movie was the notion that the first class
passengers survived at a higher rate than other passengers.
Imagine we can regard the first class passengers as a sample of the total population
on board at the time of the collision. There were 324 first class passengers of whom
62% survived the sinking. In other words our sample proportion p^ = 0:62 while n is
324. The proportion of survivors from the total population (all passengers) on board
was p = 0:38:
Using a 0.05 significance level, test whether the survival rate for first class passengers
was greater than that for all passengers. Do the six steps of the test.