One of the items that businesses would like to be able to test is whether or not a change they make to their procedures is effective. Remember that when you create a hypothesis and then test it, you have to take into consideration that some variance between what you expect and what you collect as actual data is because of random chance. However, if the difference between what you expect and what you collect is large enough, you can more readily say that the variance is at least in part because of some other thing that you have done, such as a change in procedure.

For this submission, you will watch a video about the Chi-square test. This test looks for variations between expected and actual data and applies a relatively simple mathematical calculation to determine whether you are looking at random chance or if the variance can be attributed to a variable that you are testing for.

Imagine that a company wants to test whether it is a better idea to assign each sales representative to a defined territory or allow him or her to work without a defined territory. The company expects their sales reps to sell the same number of widgets each month, no matter where they work. The company creates a null and alternate hypothesis to test sales from defined territory sales versus open sales.

One of the best ways to test a hypothesis is through a Chi-square test of a null hypothesis. A null hypothesis looks for there to be no relationship between two items. Therefore, the company creates the following null hypothesis to test: There is no relationship between the amount of sales that a representative makes and the type of territory (defined or open) that a representative works in. The alternate hypothesis would be the following: There is a relationship between the kind of sales territory a sale representative has (defined or open) and the amount of sales he or she makes during a month.

Step 1:

Watch this video.

Step 2:

Use the following data to conduct a Chi-square test for each region of the company in the same manner you viewed in the video:

Step 3:

Write an 800–1,000-word essay, utilizing APA formatting, to discuss the following:

• Describe why hypothesis testing is important to businesses.
• Report your findings from each Chi-square test that you conducted.

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.94 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.45 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

In a city, the racial make up is 68% White, 24% Black, 5% Asian and the remainder are classified as Other. A report on traffic stops by police officers in this city is being used to determine if the racial makeup of the motorists stopped reflect the racial makeup of the city. The race of drivers stopped by police officers over a 4 month period is recorded in the table. Determine if there is sufficient evidence to warrant the claim that the racial makeup of drivers in traffic stops significantly differs from the city's racial makeup.

R

ace White Black Asian Other Drivers 896 399 68 57 At the 0.025 significance level, test the claim that the racial distribution of drivers stopped in traffic stops conforms to the city's distribution of races.

The test statistic

is χ2=

The p-value is T

he conclusion is A. There is sufficient evidence to claim the racial makeup of drivers pulled over in traffic stops does not reflect the racial makeup of the city. B. There is not sufficient evidence to claim the racial makeup of drivers pulled over in traffic stops does not reflect the racial makeup of the city

Question 3: A freshman class consists of 6 students, 3 of which are girls. The class needs to select a committee of 2 to represent them in the student senate.

(1) Write the sample space of this experiment.
(2) Calculate the probability of a committee of two boys. (3) Calculate the probability of one boy and one girl.

Use Excel to Answer.

A random sample of six cars from a particular model year had the fuel consumption figures, measure in miles per gallon, shown below.

1. Using T.INV, find a 90% confidence interval for the population mean of fuel consumption for cars of this model year. Assume the distribution is normal.   (Round to 2 digits, since our raw data below are expressed with one digit.) (Show work in space provided.)

(ii) Calculate the same interval using CONFIDENCE.T. (Show work in space provided.)

(iii) Calculate the same interval using T.INV.2T.

(Note: when calculating the lower and upper bounds of the interval, do not use a rounded mean that you’ve calculated with AVERAGE. Use the unrounded mean.   Round only the final answers, which are the lower and upper bounds of the interval. Also, make sure to use STDEV.S to calculate the sample standard deviation.)

              Data:

              28.6

              18.4

              19.2

              25.8

              19.4

              20.5

A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster three centers, five guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.] Correct: Your answer is correct. lineups (b) Now suppose the roster has 3 guards, 5 forwards, 3 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 13 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.)

Multi part question needing assistance please.

1. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -1.378°C. P(Z>−1.378) _____________ ******* WHAT DO I DO ABOUT THE 8? I CAN SEE ON THE CHART THE -1.37 BUT DONT KNOW WHAT TO DO CONCERNING THE 8.

2. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 1.141°C and 2.549°C. P(1.141<Z<2.549) _______ ****HOW DO I DO TWO GIVEN NUMBERS?

3. About % of the area under the curve of the standard normal distribution is between z=−2.159 and z=2.159 (or within 2.159 standard deviations of the mean).

The following xbar and s charts based on n=4 have shown statistical control: Xba Chart: UCL=710, CL=700, LCL=690, s chart- UCL=18.08, CL=7.979, LCL=0,

A)Estimate the process parameters mean and sigma (standard deviation).

B)If the specifications are at 705+/-15, and the process output is normally distributed, estimate the fraction non conforming.

C)For the Xbar chart, find the probability of a type I error, assuming sigma is constant.

D)Suppose the process mean shifts to 693 and the standard deviation simulatneously shifts to 12. Find the probability of detecting this shift on the x bar chart on the first subsequent sample.

E)For the shift of part (D) , find the ARL.

1. 5.232608753	51.33997	1
   4.559347708	3.047033	0
   4.550088246	11.71957	1
   3.386566659	28.04548	1
   0.989064618	0.202602	0
   4.555668273	67.83218	1
   4.186405129	53.06328	1
   1.207150769	78.43352	0
   3.445792543	14.46725	1
   2.962975266	23.10411	0
   0.173612404	65.70817	0
   2.768815371	65.28198	1
   2.747367434	97.82201	1
   4.486882933	77.4523	1
   4.824678695	0.743551	0
   5.586206724	48.65186	1
   2.755386381	73.45392	1
   1.787901977	97.36504	1
   5.951385802	90.85691	1
   2.737556923	15.44293	0
   5.408894983	4.157112	0
   1.715859824	0.937882	0
   1.278844906	74.59771	0
   2.514277044	97.32341	1
   3.187058008	38.67714	1
   4.949777159	87.91089	1
   5.948802076	99.45704	1
   4.58854855	73.22006	1
   4.944593251	2.002865	0
   4.095092929	30.82503	1
   1.580255616	81.42979	1
   5.582168688	77.37155	1
   1.409875297	73.8556	1
   4.173571574	10.78412	0
   3.405384527	76.08957	1
   5.303746588	91.13028	1
   2.646338619	30.76739	0
   5.648448558	24.47563	0
   5.460162608	6.448907	1
   2.530400279	92.75311	1
   5.282410782	26.05696	1
   4.798709185	42.12116	1
   4.300055705	57.20119	1
   4.729502404	6.523547	0
   2.476612604	55.6309	1
   3.190133005	67.05927	1
   1.021463153	77.07357	1
   0.733750098	95.86227	1
   2.724156232	4.533329	0
   4.232730005	96.12467	1

   For a column of data x and a column of data y, there is an equation that relates the slope of the line of best fit (m) with the correlation coefficient (r). That equation is:

m = r * std(y)/std(x)

In the equation above, std(y) represents the standard deviation of the y column of data and std(x) is the standard deviation of the x column of data.

Use the Pandas .corr() and .std() methods to compute the slope of the line of best fit between Diameter and Pigment（first & second col）.

Next, use compute the y-intecept of the line of best fit using:

b = ybar – m*xbar

         Lastly, plot the line of best fit using matplotlib.pyplot.

6 a) You and your friend are in a class with 12 students. For a project, the class is randomly divided into two equal groups. “Randomly” means all divisions are equally likely. What is the probability that you and your friend end up in the same group?

6 b) Revisit part a). Calculate the probability that you and your friend will end up in the same group if the class is divided into three equal groups instead.

Suppose that you want to improve the process of loading passengers onto an airplane. Would a discrete event simulation model of this process be useful? What data would have to be collected to build this model?

Investment advisors might subscribe to the Business Times (BT) or Straits Times (ST). For those investment advisors who subscribe to at least one of the papers, one-third subscribe to only one newspaper, ST, and one-fourth subscribe to only one newspaper, BT. 40% of the investment advisors subscribe to both papers. (a) Complete the probability table below (the grey boxes).

BT BTC TOTAL

ST

STC

TOTAL 1

Total 1.0 (b) Suppose an investment advisor receives at least one of the papers. What is the probability they receive the BT?

The Hillsboro Aquatic Centre has an indoor pool with lanes for lap swimming and an open area for recreational swimming and various exercise and water aerobics programs. From 1 June to mid-August it operates on a summer schedule, and from mid-August to the end of May it operates according to normal weekday and weekend schedules. The centre’s policy for the pool is to have a lifeguard-to-patron ratio of 1:40. The centre director wants to develop a forecast of pool attendance for the weekday schedule in order to determine the number of lifeguards to hire. The following data for average daily attendance for each hour of the day that the pool is open to the public (i.e., there are no swim team practices):

Develop a seasonally adjusted forecast model for these data for hourly pool attendance. Forecast attendance for each hour for year 7 by using a linear trend line estimate for pool attendance in year 7. Do the data appear to have a seasonal pattern?

The government conducts a survey of the population and finds that 208 of 681 respondents report voting for party A last election, and 284 of 512 respondents report voting for party A for the next election. If you are conducting a hypothesis testing with a null hypothesis of p1=p2{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>1</mn></msub><mo>=</mo><msub><mi>p</mi><mn>2</mn></msub></math>"}, calculate p{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>p</mi></menclose></math>"} .