Cathy Keene has just started a new business for design and manufacturing of reusable protective face masks. Due to the high demand, Cathy wants to invest in a new production machine. She considers Machine K and Machine S, but before making the final decisions, Cathy wants to compare their errors. To do so, Cathy asks the manufacturers to provide a sample of the recorded number of errors per day.

Machine K

Machine S

At 0.05 significance level, test whether there is a significant difference between the variances in the number of errors of the two machines.

Use the above information to answer the following questions:

The required test statistics is: Answer .

This a Answer –tail test.

The sample mean number of errors for Machine K is Answer

The sample mean number of errors for Machine S is Answer

The sample standard deviation for Machine K is Answer (rounded to four decimal places)

The sample standard deviation for Machine S is Answer (rounded to four decimal places)

The critical value is Answer

The calculated test statistics is Answer (rounded to four decimal places)

The statistical decision is: Answer

The conclusion is: Answer

According to the 2017 SAT Suite of Assessments Annual Report, the average ERW (English, Reading, Writing) SAT score in Florida was 520. Assume that the scores are Normally distributed with a standard deviation of 100. Answer the following including an appropriately labeled and shaded Normal curve for each question.

a) What is the probability that an ERW SAT taker in Florida scored 500 or less?

b) What percentage of ERW SAT takers in Florida scored between 500 and 650?

c) What ERW SAT score would correspond with the 40th percentile in Florida?

1. Professor Heinz has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 69 and a standard deviation of 19. Use an appropriate normal transformation to Calculate the probability that a class of 36 students will have an average greater than 60 on Professor Heinz's final exam.

2. Professor Heinz has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 69 and a standard deviation of 19. Calculate the probability that a class of 36 students will have an average greater than 60 on Professor Heinz's final exam.

5. The average age of a vehicle registered in the United States is 8 years, or 96 months. If a random sample of 36 vehicles is selected, find the probability that the mean of their age is between 98 and 100 months? Assume the standard deviation for the population is 15.

Below are revenue and profit (both in $ billions) for nine large entertainment companies. Revenue and Profit of Nine Entertainment Companies (See the attached Excel file for correct, readable format)

Company Revenue Profit

AMC Entertainment 1.792 -0.020

Clear Channel Communication 8.931 1.146

Liberty Media 2.446 -0.978 Metro-

Goldwyn-Mayer 1.883 -0.162

Regal Entertainment Group 2.490 0.185

Time Warner 43.877 2.639

Univision Communications 1.311 0.155

Viacom 26.585 1.417

Walt Disney 27.061 1.267

Correlation and Regression

Make a scatterplot of profit as a function of revenue. Use Excel to fit the Trendline to the above problem data. Display the Regression Equation and R2. Explain the meaning of the Regression Equation and the R2. How would this model be applied to financial analysis and forecasting?

In 2013, 30% of business owners gave a holiday gift to their employees. A 2014 survey of 53 business owners indicated that 19% plan to provide a holiday gift to their employees. Is there reason to believe the proportion of business owners providing gifts has decreased at a=0.05?

1)- What is/are the critical values?

2)- What is the test statistics?

3)- What is the conclusion?

Please explain in detail and step by step

A process that manufactures glass sheets is supposed to be calibrated so that the mean thickness  of the sheets is more than 4 mm. The standard deviation of the sheet thicknesses is known to be well approximated by σ = 0.20 mm. Thicknesses of each sheet in a sample of sheets will be measured, and a test of the hypothesis H_0:μ≤4 versus H_1:μ>4 will be performed. Assume that, in fact, the true mean thickness is 4.04 mm.

a) If 100 sheets are sampled, what is the power of a test made at the 5% level?

b) How many sheets must be sampled so that a 5% level test has power 0.95?

c) If 100 sheets are sampled, at what level must the test be made so that the power is 0.90?

d) If 100 sheets are sampled, and the rejection region is X ̅≥4.02, what is the power of the test?

Following is the normalized distance matrix for the first four records of the Excel file Credit Approval Decisions. Apply single linkage clustering to these records until only one option remains. What conclusions can you make from this analysis?

This data set presents 17 paired data corresponding to the weights of girls before and after treatment for anorexia.

a. What is the appropriate t-test?

b. What are the dependent and independent variables?

c. State the null and alternative hypothesis.

d. For α =.05, two tailed, what is the degrees of freedom and t_crit?

df =

t_crit =)

d. What is t_obs? (Show the calculation. Show SS calculation)

e. Calculate 95% confidence interval of the mean difference (Show the calculation.)

f. Write your conclusion as it would appear in a research paper. Report t-statistic (don’t forget to put the df), p-value, and the 95% confidence interval that support your decision.

Question 3: Suppose the height for girls is distributed normally with a mean (μ₁) of 66 inches and a standard deviation of 3.5 inches. The height for boys is distributed normally with a mean (μ₂) of 68 inches and a standard deviation of 4 inches.

a) Using R, simulate a sample of n₁ = 50 boys and n₂ = 50 girls and compute ?̅₁ − ?̅₂. Repeat 5,000 times. Plot the histogram of the sampling distribution of ?̅₁ − ?̅₂.

b) Estimate Var(?̅₁ − ?̅₂) based on the results of your simulation. Does this match the expected variance of ?̅₁ − ?̅₂?

c) Compute a 95% confidence interval for the difference of the means (μ₁ - μ₂). What percentage of the time does the 95% confidence interval contain the true difference in (μ₁ - μ₂) of -2? Assume unequal variances.

d) Compute a 95% confidence interval for the difference of the means (μ₁ - μ₂). What percentage of the time does the 95% confidence interval contain the true difference in (μ₁ - μ₂) of -2? Assume equal variances.

e) Compare your results in (c) and (d).

A researcher was interested in investigating a relationship between the age (independent variable) of a driver and the distance the driver can see. For this purpose, he collected data on some drives. The data is provided in Appendix ‘1”.

To help you, partial summary analysis is provided below: SSxx= 13,752 SSxy=- 41,350 SSyy=193,667 ∑ x = ∑ Age = 1,530; ∑ y = ∑(Distance the driver can see)=12,700

Age Distance
18 510
20 590
22 560
23 510
23 460
25 490
27 560
28 510
29 460
32 410
37 420
41 460
46 450
49 380
53 460
55 420
63 350
65 420
66 300
67 410
68 300
70 390
71 320
72 370
73 280
74 420
75 460
77 360
79 310
82 360

a) Write the estimated regression line

b) Is the relationship meaningful (significant at α=0.05)? (3 pts) – make sure to state the null and alternative hypothesis first.

c) What is the strength of the relation? It is significant? (3 pts)

d) What is the coefficient of determination? (2 pts)

e) John is 61 years old. What is the expected driving distance for him? What is the 95% prediction interval for John? (4 pts)

A medical examination tests the presence of viruses in human bodies. Here,

H0: The viral load equals zero (i.e., virus not present) and

Ha: The viral load is larger than zero (i.e., virus present).

3.1 What would be a Type I error?  

3.2 What would be a Type II error?

3.3 Two methods of testing are available: Test A sets the bar to reject the null high (i.e.,

harder to reject), whereas Test B sets the bar to accept the null high. Assuming the virus

is highly infectious and potentially deadly, which test would you choose, and why?

what is the relationship between linear, multiple and logistic regrerssion

According to the credit rating agency Equifax, credit limits on newly issued credit cards increased between January 2011 and May 2011. Suppose that random samples of 400 new credit cards issued in January 2011 and 500 new credit cards issued in May 2011 had average credit limits of $2635 and $2887, respectively. Suppose that the sample standard deviation for these two samples were $365 and $412 respectively. Assume that the population standard deviations for the two populations are unknown and unequal. a) Let ?1 and ?2 be the average credit limits on all credit cards issued in January 2011 and in May 2011, respectively. Construct a 98% confidence interval for ?1 −?2. b) At a 1% significance level, can you conclude that the average credit limit for all new credit cards issued in January 2011 was lower than the corresponding average for all credit cards issued in May 2011? Use both the P-value approach and the critical value approach to make this test.

Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 5% for home loans, 12% for personal loans, and 11% for automobile loans. The bank’s planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.