Search concept of Degrees of Freedom in statistics to explain what it is. Make sure to provide a couple of examples as to how it is applied. Short Paragraph.

4. Overhead Door (OD) Corporation’s founder, C. G. Johnson, invented the upward-lifting garage door in 1921 and the electric garage door opener in 1926. Since then OD has been a leading supplier of commercial, industrial, and residential garage doors sold through a nationwide network of more than 450 authorized distributors. They have built a solid reputation as a premier door supplier, commanding 15 % share of the market.

Suppose that customers assess door quality first in terms of the ease of operation, followed by its durability. The quality improvement team (QIT) might then assign an engineering team to determine the factors that contribute to these two main problems.

Smooth operation of a garage door is a critical quality characteristic that affects both problems: If a door is too heavy, it’s difficult and unsafe to balance and operate; if it’s too light, it tends to buckle and break down frequently or may not close properly.

Suppose the design engineers determine that a standard garage door should weigh a minimum of 74 kg. and a maximum of 86 kg., which thus specifies its design quality specification. QIT is inspecting if there is evidence that the percentage of defective doors does not exceed 7%. Suppose the QIT decides to collect data on the actual weights of 60 standard garage doors sampled randomly from their monthly production of almost 2,000 doors. See the tables on the next page.

4.1 (2 point) What is the sample defective rate ?

4.2 (2 points) Formulate and test an appropriate set of hypotheses to determine if the machine can be qualified. Use α = 0.05. Find the P-value.

4.3 (2 points) What is the 95% confidence interval?

4.4 (2 points) What is the 99% confidence interval?

Table 2:

1a. Consider two samples from the same population. Sample A has size n=500 and Sample B has size n = 200. Indicate whether each of the following statements is true or false.

1b. Consider a p% confidence interval (CI) for the population mean constructed from a sample of size n. (For example, if p is 95 then it’s a 95% confidence interval.) Indicate whether each of the following statements is true or false.

ANSWER ALL PARTS WITH TRUE OR FALSE.

Samples of n = 5 units are taken from a process every hour. The x-bar and R-bar values for a particular quality characteristic are determined. After 25 samples have been collected, we calculate x-bar = 20 and R-bar = 4.56. a) What are the three-sigma control limits for x-bar and R? b) Both charts exhibit control. Estimate the process standard deviation. c) Assume that the process output is normally distributed. If the specifications are 19 ± 5, what are your conclusions regarding the process capability? d) If the process mean shifts to 24, what is the probability of not detecting this shift on the first subsequent sample? .I want expert solution

se technology to find the​ P-value for the hypothesis test described below.

The claim is that for 12 AM body​ temperatures, the mean is

muμgreater than>98.6degrees°F.

The sample size is

nequals=5

and the test statistic is

tequals=1.078.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

The manufacturer of an MP3 player wanted to know whether a 10% reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP3 player was sold at the regular price. Reported below is the number of units sold last month at the regular and reduced prices at the randomly selected outlets.

  Click here for the Excel Data File

At the 0.050 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales? Hint: For the calculations, assume reduced price as the first sample.

1. Compute the pooled estimate of the variance. (Round your answer to 3 decimal places.)

2. Compute the test statistic. (Round your answer to 2 decimal places.)

3. State your decision about the null hypothesis.

• Fail to reject H₀

• Reject H₀

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 315 accurate orders and 63 that were not accurate. a.) Construct a 95​% confidence interval estimate of the percentage of orders that are not accurate. b.) Compare the results from part​(a) to this 90​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.144< p < 0.226. What do you​ conclude?

a) Construct a 90% confidence interval. Express the percentages in decimal form.

I want examples on paired-sample sign test (one for small sample and one for large sample)

You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes.

A) Using the six-step critical value approach, at the 0.05 level of significance, is there evidence that the population mean delivery time has been reduced below the previous population mean value of 25 minutes?
B) At the 0.05 level of significance, use the five-step P-value approach.
C) Interpret the meaning of the P-value in (b).
D) Compare your conclusions in (a) and (b).

A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to protect the population for a mean time of 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 21 people were given the new shot. Regular blood tests showed that the sample standard deviation of protection times was 1.3 months. Using a 0.05 level of significance, test the claim that the new typhoid shot has a smaller variance of protection times.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 9; H₁: σ² > 9H_o: σ² = 9; H₁: σ² < 9    H_o: σ² < 9; H₁: σ² = 9H_o: σ² = 9; H₁: σ² ≠ 9

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a uniform population distribution.We assume a exponential population distribution.    We assume a binomial population distribution.We assume a normal population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

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

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 insufficient evidence to conclude that the new typhoid shot has a smaller variance of protection times.At the 5% level of significance, there is sufficient evidence to conclude that the new typhoid shot has a smaller variance of protection times.    

(f) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

Interpret the results in the context of the application.

We are 90% confident that σ lies within this interval.We are 90% confident that σ lies below this interval.    We are 90% confident that σ lies above this interval.We are 90% confident that σ lies outside this interval.

1) Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, four green ones, two white ones, and one purple one. She grabs five of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.] She has two green ones and one of each of the other colors.

2) Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, three green ones, four white ones, and two purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.] She does not have all the red ones.

3) Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, four green ones, three white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.] She does not have all the green ones.

a box contains two red balls , one white ball and one blue ball. A sample of two balls was drawn randomly, respectively (without return), If the variable X express the number of white balls and the variable Y express the number of blue balls in the sample, find :

A- Fxy(0,1)

B- Coefficient of correlation between the two variables and then commented on it

BOB’S SERVICE STATION AND DINER “Sylvia, we have been operating this service station and diner for many years. Lately, I have the feeling that my income has declined. I think that there are opportunities out there that I have not taken advantage of. I want to pass this business on to my sons and am not comfortable with our current position and strategy.” The words above, spoken to Sylvia, the primary accountant for Bob’s, reveal a number of concerns Bob has concerning his operation. Bob’s Service Station and Diner (Bob’s) is an independently owned service station and restaurant on a major interstate highway. Bob has been in operation for over a decade and customers have liked to frequent his business. Often they choose their routes to stop at places like his with low fuel prices and to enjoy food like the juicy burgers and good food Bob’s provides. He has a great reputation with his customers, especially truckers, and enjoys their business. Bob has noticed, however, that when busiest with truckers, fewer families stop by. Bob has made a pretty good living running the place. However, even though his income continues to seem satisfactory, it does not seem to buy as much as before. This perception, as well as the maturity of his sons, Jason and Bob Jr., has heightened Bob’s concern over the future of his operation. Bob wants to know what he can do to make this a more profitable business and pass on a more effective operation to his sons. Bob knows that his operation attracts many commercial truckers. However, he is also popular with families stopping to use the facilities and eat in the restaurant after filling up the family vehicle on vacations. Over the past decade Bob’s typical markup on diesel is about 1 cent and on gasoline is about 1.5 cents. This fuel pricing follows the typical process in this business of taking the delivery price and marking it up between 1 and 5 cents per gallon. Bob has also noticed an ebb and flow by season – summer and winter being highest and spring and fall being lower. (Winter is December, January, February. Summer is June, July and August.) Bob knows that he has some control over fuel prices and can alter the prices of his typical meal. The dilemma he faces is to know in what direction he should change them or whether or not he should modify his pricing practice at all. Also, he does not know what other activities or attractions he could add that might increase his profits. If he raises prices, he knows that he will reduce sales. At lower prices, he will sell more but incur greater costs. Bob is getting ready to step back from his business and turn the operation over to his sons. Before he does that, he wants to be comfortable in leaving his sons with a well-defined pricing strategy, based upon data. Following up on the expression of Bob’s future concerns, Sylvia, his accountant, has gathered a substantial amount of information regarding his firm’s performance over the past decade. This data is available in an Excel file on the course web site.

QUESTION: Use simple regression to estimate the marginal profit contribution from fuel sales. Use it again to estimate the marginal profit contribution from food sales. Compare and interpret your estimates.

Please find DATA here:

https://www.csun.edu/~ba44982/BUS302%20-%20Spring%202020/Case5/Bob's%20Service%20Station%20and%20Diner%20-%20Student%20Data%20Spreadsheet%20-%20rev%201.xlsx

Barbara Lynch, the product manager for a line of skiwear produced by HeathCo Industries, has been working on developing sales forecasts for the skiwear that is sold under the Northern Slopes and Jacque Monri brands. She has had various regression-based forecasting models developed. Quarterly sales for 1988Q1 through 1997Q4 are as follows:

a) Prepare a time-series plot of the data, and on the basis of what you see in the plot, write a brief paragraph in which you explain what patterns you think are present in the sales series.

b) Smooth out seasonal influences and irregular movement by calculating the center moving averages. Add the centered moving averages to the original data you plotted in part a. Has the process of calculating center moving averages been effective in smoothing out the seasonal and irregular fluctuations in the data? Explain.

c) Determine the degree of seasonality by calculating seasonal indexes for each quarter of the year.

d) Develop a forecast for Ms Lynch for the four quarters of 1998.