The Apex corporation produces corrugated paper. It has collected monthly data from January 2001 through March 2003 on the following two variables:

y= total manufacturing cost per month (In thousands of dollars) (COST)

x= total machine hours used per month (Machine)

The data are shown below.

1102 218
1008 199
1227 249
1395 277
1710 363
1881 399
1924 411
1246 248
1255 259
1314 266
1557 334
1887 401
1204 238
1211 246
1287 259
1451 286
1828 389
1903 404
1997 430
1363 271
1421 286
1543 317
1774 376
1929 415
1317 260
1302 255
1388 281

Answer the following question

Fill in the blanks for the following statement: “I am 95% confident that the average manufacturing cost at the Apex corporation for all months with 350 total machine hours is between ____ and ____.”

please show me steps

You Explain it:

1. What is a residual?
2. What does it mean when a residual is positive?
3. Explain the phrase outside the scope of the model.
4. Why is it dangerous to make predictions outside the scope of the model?
5. Explain what each point on the least-squares regression line represents.

1. 7-31 Consider the following LP problem:

Maximize profit=5X+6Y

subject to2X+Y≤120, 2X+3Y≤240X,Y≥0

1. What is the optimal solution to this problem? Solve it graphically.
2. If a technical breakthrough occurred that raised the profit per unit of X to $8, would this affect the optimal solution?
3. Instead of an increase in the profit coefficient X to $8, suppose that profit was overestimated and should only have been $3. Does this change the optimal solution?

1. 7-32 Consider the LP formulation given in Problem 7-31. If the second constraint is changed from 2X + 3Y≤2402X + 3Y≤240 to 2X+4Y≤240,2X+4Y≤240, what effect will this have on the optimal solution?

"Trydint" bubble-gum company claims that 3 out of 10 people prefer their gum to "Eklypse". Test their claim at the 99 confidence level. The null and alternative hypothesis in symbols would be: H 0 : p ≤ 0.3 H 1 : p > 0.3 H 0 : μ = 0.3 H 1 : μ ≠ 0.3 H 0 : μ ≥ 0.3 H 1 : μ < 0.3 H 0 : μ ≤ 0.3 H 1 : μ > 0.3 H 0 : p = 0.3 H 1 : p ≠ 0.3 H 0 : p ≥ 0.3 H 1 : p < 0.3 The null hypothesis in words would be: The average of people that prefer Trydint gum is not 0.3. The proportion of all people that prefer Trydint gum is less than 0.3. The proportion of people in a sample that prefers Trydint gum is 0.3. The proportion of people in a sample that prefer Trydint gum is not 0.3 The proportion of all people that prefer Trydint gum is greater than 0.3. The proportion of all people that prefer Trydint gum is 0.3 The average of people that prefer Trydint gum is 0.3. Based on a sample of 280 people, 58 said they prefer "Trydint" gum to "Eklypse". The point estimate is: (to 3 decimals) The 99 % confidence interval is: to (to 3 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis

2. Problem 2 is adapted from the Problem 39 at the end of Chapter 11. Please solve this problem in Excel and submit your Excel spreadsheet. The problem is as follows: The state of Virginia has implemented a Standard of Learning (SOL) test that all public school students must pass before they can graduate from high school. A passing grade is 75. Montgomery County High School administrators want to gauge how well their students might do on the SOL test, but they don't want to take the time to test the whole student population. Instead, they selected 20 students at random and gave them the test. The results are as follows: 83 79 56 93 48 92 37 45 72 71 92 71 66 83 81 80 58 95 67 78 Assume that SOL test scores are normally distributed. a. Compute the mean and standard deviation for these data. b. Determine the probability that a student at the high school will pass the test. c. How many percent of students will receive a score between 75 and 95? d. What score will put a student in the bottom 15% in SOL score among all students who take the test? e. What score will put a student in the top 2% in SOL score among all students who take the test? 3. The average male drinks 2 L of water when active outdoors (with a standard deviation of 0.8L). You are planning a full day nature trip for 100 men and will bring 210 L of water. What is the probability that you will run out? Please solve this problem in Excel and submit your Excel file.

Consider two independent random samples with the following results: n 1 =160 x 1 =84     n 2 =95 x 2 =72 Use this data to find the 90% confidence interval for the true difference between the population proportions. Copy Data Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places.

in a clinical trial, 25 out of 852 patients taking a prescription drug daily complained of flulike symptoms. Suppose that is it known that 2.5% of patients taking competing drugs complain of flulike symptoms. is there enough evidence to conclude that more than 2.5% of this drugs users experience flulike symptoms as a side effect at the 0.1 level of significance?

Here are summary statistics for randomly selected weights of newborn​ girls: n=187​, x =30.8 ​hg, s=7.9 hg. Construct a confidence interval estimate of the mean. Use a 90​% confidence level. Are these results very different from the confidence interval 29.0 hg-mu-t32.4 hg with only 14 sample​ values, x=30.7 ​hg, and s=3.6 ​hg

At one point the average price of regular unleaded gasoline was $3.53 per gallon. Assume that the standard deviation price per gallon is ​$0.07

per gallon and use​ Chebyshev's inequality to answer the following.

​(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean? What are the gasoline prices that are within 2.5 standard deviations of the​ mean?

​(c) What is the minimum percentage of gasoline stations that had prices between $3.39 and $3.67​?

​(a) At least _​__% of gasoline stations had prices within 3 standard deviations of the mean.(Round to two decimal places as​ needed.)

​(b) At least ___% of gasoline stations had prices within 2.5 standard deviations of the mean.​(Round to two decimal places as​ needed.)

The gasoline prices that are within 2.5 standard deviations of the mean are ​$_to ​$_.​(Use ascending​ order.)

​(c) _​__% is the minimum percentage of gasoline stations that had prices between $ 3.39 and $3.67.

There are 3 coins which when flipped come up heads, respectively, with probabilities 1/4, 1/2, 3/4. One of these coins is randomly chosen and continually flipped.

1. (a) Find the expected number of flips until the first head.

2. (b) Find the mean number of heads in the first 8 flips.

The standard deviation alone does not measure relative variation. For example, a standard deviation of $1 would be considered large if it is describing the variability from store to store in the price of an ice cube tray. On the other hand, a standard deviation of $1 would be considered small if it is describing store-to-store variability in the price of a particular brand of freezer. A quantity designed to give a relative measure of variability is the coefficient of variation. Denoted by CV, the coefficient of variation expresses the standard deviation as a percentage of the mean. It is defined by the formula CV = 100(s/ x ). Consider two samples. Sample 1 gives the actual weight (in ounces) of the contents of cans of pet food labeled as having a net weight of 8 oz. Sample 2 gives the actual weight (in pounds) of the contents of bags of dry pet food labeled as having a net weight of 50 lb. There are weights for the two samples.

(a) For each of the given samples, calculate the mean and the standard deviation. (Round all intermediate calculations and answers to five decimal places.)

(b) Compute the coefficient of variation for each sample. (Round all answers to two decimal places.)

1. A company uses three different assembly lines – A1, A2, and A3 – to manufacture a particular component. Of those manufactured by line A1, 5% need rework to remedy a defect, whereas 8% of A2’s components need rework and 10% of A3’s need rework. Suppose that 50% of all components are produced by line A1, 30% are produced by line A2, and 20% come from line A3.

   1. (a) Suppose a component is selected at random, what is the probability that it needs rework?

   2. (b) If a randomly selected component needs rework, what is the probability that it came from line A1?

   3. (c) If a randomly selected component (((((((does not))))))) need rework, what is the proba- bility that it came from line A2?

You are a professor of statistics and have been asked to teach a course in social science statistics off-campus to a class of grad students enrolled in the Continuing Education Program of the University. Since you’ve never taught this program before, you don’t know a great deal about the needs and background of the students in the class. In order to learn more, you hand out a survey to each student asking for information on the following variables: age, undergraduate field, number of stats courses taken, and the level of interest in conducting research (coded as low, medium, high). The results are below:

Analyze your data to give you some useful information about the class. In doing so you need to answer a few things: the level of measurement of the variables, meaningful measures of central tendency for each variable (there can be more than one), the calculated measure of central tendency for each variable (there can be more than one). In order to do that, populate the following table:

Based on the data you collected, calculate the measures of dispersion (specifically the range, variance and standard deviation) for each of the variables that are at the interval level of measurement.

Since all of your data, your measures of central tendency and measures of dispersion. brief paragraph explaining the results of your survey paying special attention to what you, as the instructor, would find useful to bear in mind as you conduct the class. Address each variable, meaningful measures of central tendency for each (providing brief mention as to why you think which are the most useful), and measures of dispersion (where appropriate). You can include graphical representations of the data where it would help to defend the answer.

1. A custodian wishes to compare two competing floor waxes to decide which one is best. He believes that the mean of WaxWin is not equal to the mean of WaxCo. In a random sample of 37 floors of WaxWin and 30 of WaxCo. WaxWin had a mean lifetime of 26.2 and WaxCo had a mean lifetime of 21.9. The population standard deviation for WaxWin is assumed to be 9.1 and the population standard deviation for WaxCo is assumed to be 9.2. Perform a hypothesis test using a significance level of 0.10 to help him decide. Let WaxWin be sample 1 and WaxCo be sample 2. The correct hypotheses are: H 0 : μ 1 ≤ μ 2 H 0 : μ 1 ≤ μ 2 H A : μ 1 > μ 2 H A : μ 1 > μ 2 (claim) H 0 : μ 1 ≥ μ 2 H 0 : μ 1 ≥ μ 2 H A : μ 1 < μ 2 H A : μ 1 < μ 2 (claim) H 0 : μ 1 = μ 2 H 0 : μ 1 = μ 2 H A : μ 1 ≠ μ 2 H A : μ 1 ≠ μ 2 (claim) Correct

Since the level of significance is 0.10 the critical value is 1.645 and -1.645

The test statistic is: Incorrect(round to 3 places)

The p-value is: Incorrect(round to 3 places)

A random sample of 30 chemists from Washington state shows an average salary of $42546, the population standard deviation for chemist salaries in Washington state is $868. A random sample of 39 chemists from Florida state shows an average salary of $48395, the population standard deviation for chemist salaries in Florida state is $945. A chemist that has worked in both states believes that chemists in Washington make more than chemists in Florida. At αα=0.05 is this chemist correct?

Let Washington be sample 1 and Florida be sample 2.

The correct hypotheses are:

• H0:μ1≤μ2H0:μ1≤μ2
  HA:μ1>μ2HA:μ1>μ2(claim)
• H0:μ1≥μ2H0:μ1≥μ2
  HA:μ1<μ2HA:μ1<μ2(claim)
• H0:μ1=μ2H0:μ1=μ2
  HA:μ1≠μ2HA:μ1≠μ2(claim)

Since the level of significance is 0.05 the critical value is 1.645
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)

A researcher is interested in seeing if the average income of rural families is greater than that of urban families. To see if his claim is correct he randomly selects 45 families from a rural area and finds that they have an average income of $66299 with a population standard deviation of $668. He then selects 31 families from a urban area and finds that they have an average income of $67979 with a population standard deviation of $534. Perform a hypothesis test using a significance level of 0.01 to test his claim. Let rural families be sample 1 and urban familis be sample 2.

The correct hypotheses are:

• H0:μ1≤μ2H0:μ1≤μ2
  HA:μ1>μ2HA:μ1>μ2(claim)
• H0:μ1≥μ2H0:μ1≥μ2
  HA:μ1<μ2HA:μ1<μ2(claim)
• H0:μ1=μ2H0:μ1=μ2
  HA:μ1≠μ2HA:μ1≠μ2(claim)

Since the level of significance is 0.01 the critical value is 2.326
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)

A researcher is interested in seeing if the average income of rural families is greater than that of urban families. To see if his claim is correct he randomly selects 45 families from a rural area and finds that they have an average income of $66299 with a population standard deviation of $668. He then selects 31 families from a urban area and finds that they have an average income of $67979 with a population standard deviation of $534. Perform a hypothesis test using a significance level of 0.01 to test his claim. Let rural families be sample 1 and urban familis be sample 2.

The correct hypotheses are:

• H0:μ1≤μ2H0:μ1≤μ2
  HA:μ1>μ2HA:μ1>μ2(claim)
• H0:μ1≥μ2H0:μ1≥μ2
  HA:μ1<μ2HA:μ1<μ2(claim)
• H0:μ1=μ2H0:μ1=μ2
  HA:μ1≠μ2HA:μ1≠μ2(claim)

Since the level of significance is 0.01 the critical value is 2.326
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)