By utilising Annexure A, answer the following questions:

1. 15 samples of n = 8 have been taken from a cleaning operation. The average sample range for the 20 samples was 0.016 minutes, and the average mean was 3 minutes. Determine the three-sigma control limits for this process.
2. 15 samples of n = 10 observations have been taken from a milling process. The average sample range is 0.01 centimetres. Determine upper and lower control limits for sample ranges
3. Determine which of these three processes are capable
   

Carson Trucking is considering whether to expand its regional service center in​ Mohab, UT. The expansion requires the expenditure of $10,500,000 on new service equipment and would generate annual net cash inflows from reduced costs of operations equal to $4,000,000 per year for each of the next 7 years. In year 7 the firm will also get back a cash flow equal to the salvage value of the​ equipment, which is valued at $1.1 million. ​ Thus, in year 7 the investment cash inflow totals $5,100,000. Calculate the​ project's NPV using a discount rate of 7 percent.   

If the discount rate is 7 percent, then the​ project's NPV is $ ___

We want to test the claim that people are taller in the morning than in the evening. Morning height and evening height were measured for 30 randomly selected adults and the difference (morning height) − (evening height) for each adult was recorded in the table below. Use this data to test the claim that on average people are taller in the morning than in the evening. Test this claim at the 0.01 significance level.

DATA ( n = 30 )
AM-PM Height
Difference

The following data come from the 2016 ANES, V36 and V87W, both recoded into 3 categories. One question asked about party identification. The other asked about support for building a wall on the border between the United States and Mexico.  The results were as follows:

Calculate appropriate percentages for the table, justify your choice of row, column, or total percentages, and comment on the relationship.

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use  = .05.

1. Complete the following ANOVA table (to 2 decimals, if necessary). Round p-value to four decimal places.

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
   Factor A
   Factor B
   Interaction
   Error
   Total

   
   
2. The p-value for Factor A is Selectless than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 21
   
   What is your conclusion with respect to Factor A?
   SelectFactor A is significantFactor A is not significantItem 22
   
3. The p-value for Factor B is Selectless than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 23
   
   What is your conclusion with respect to Factor B?
   SelectFactor B is significantFactor B is not significantItem 24
   
4. The p-value for the interaction of factors A and B is Selectless than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 25
   
   What is your conclusion with respect to the interaction of Factors A and B?
   SelectThe interaction of factors A and B is significantThe interaction of factors A and B is not significantItem 26

A high school teacher hypothesizes a negative relationship between performance in exams and performance in presentations. To examine this, the teacher computes a correlation of 0.58 from a random sample of 18 students from class. What can the teacher conclude with an α of 0.01?

a) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

b) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

c) Make an interpretation based on the results.

There is a significant positive relationship between performance in exams and performance in presentations.There is a significant negative relationship between performance in exams and performance in presentations.    There is no significant relationship between performance in exams and performance in presentations.

a human resource survey revealed that 30% of job applicants cheat on their psychometric test. use the binomial formula to find the probability that the number of job applicants in a sample of 14 who cheat on their psychometric test is:

a. exactly 8

b. less than 2

c. at least 1

A clinical trial is conducted comparing a new pain reliever for arthritis to a placebo. Participants are randomly assigned to receive the new treatment or a placebo and the outcome is pain relief within 30 minutes. The data are shown here.

Is there a significant difference in the proportions of

patients reporting pain relief?

Run the test at a 5% level of significance.

H0: p1= p2(equivalent to RD = 0, RR=1 or OR=1)

Can they reject the H_0?

Group of answer choices

Yes, Reject H0, there is a statistically significant difference in the proportions of patients reporting pain relief in the new medication and placebo groups

No, Fail to Reject H0, there is no statistically significant difference in the proportions of patients reporting pain relief between the new medication and placebo groups

Not enough information to answer this research question

perform Levene’s test for equal variance. Note, this is a one‐way ANOVA testing for the equality of 16 variances (each combination of promotion/discount). 0.1 signigicance

2. perform 2-way anova with replication

To answer these questions, an experiment was designed using laundry detergent pods. For ten weeks, 160 subjects received information about the products. The factors under consideration were the number of promotions (1, 3, 5, or 7) that were described during this ten‐ week period and the percent that the product was discounted (10%, 20%, 30%, or 40%) off the average non‐promotional price. Ten individuals were randomly assigned to each of the sixteen combinations. The data reflecting what the sub‐ jects would expect to pay for the product (i.e., their reference price) at the end of the 10‐week period. 0.1 significance

To characterize random uncertainty of a pressure measuring technique, twelve pressure measurements were made of a certain constant pressure source, giving the following results in kPa: 125, 128, 129, 122, 126, 125, 125, 130, 126, 127, 124, and 123. (a) Estimate the 95% confidence interval of the next measurement obtained with this technique; (b) Estimate the 95% confidence interval of the average of next 5 measurements obtained with this technique; (c) Using only the 12 measurements available, how would you report the value of measured pressure, including the 95% confidence interval?

Consider a Bernoulli random variable X such that P(X=1) = p. Calculate the following and show steps of your work:

a) E[X]

b) E[X²]

c) Var[X]

d) E[(1 – X)¹⁰]

e) E[(X – p)⁴]

f) E[3^x4^1-x]

g) var[3^x4^1-x]

1-what is the dummy variable and what is the purpose of included in regression model ?

2- explaining the meaning of adjust r square?

3-if adjust r square computed. would it be higher , equal of lower than value of r square?

The U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542. Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246. A Boston worker is randomly selected. (Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

(a) What is the probability that the worker’s annual salary is more than $60,000?

(b) What is the probability that the worker’s annual salary is less than $42,000?

(c) What is the probability that the worker’s annual salary is more than $39,000?

(d) What is the probability that the worker’s annual salary is between $43,000 and $51,000?

A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 20 residents in that town has a mean credit card debt of $3619 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported?

The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.

Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Ceremonial ranking and pottery type are not independent.
H₁: Ceremonial ranking and pottery type are not independent.

H₀: Ceremonial ranking and pottery type are independent.
H₁: Ceremonial ranking and pottery type are not independent.    

H₀: Ceremonial ranking and pottery type are not independent.
H₁: Ceremonial ranking and pottery type are independent.

H₀: Ceremonial ranking and pottery type are independent.
H₁: Ceremonial ranking and pottery type are independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

Student's t

uniform    

normal

chi-square

binomial

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.100

0.050 < p-value < 0.100    

0.025 < p-value < 0.050

0.010 < p-value < 0.025

0.005 < p-value < 0.010

p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.   

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.

At the 5% level of significance, there is insufficient evidence to conclude that ceremonial ranking and pottery type are not independent.