A real estate agent wants to study the relationship between the size of an apartment and its monthly rent price. The table below presents the size in square feet and the monthly rent in dollars, for a sample of apartments in a suburban neighborhood.

Calculate the correlation between these two variables.

If a linear regression model were fit, what is the value of the slope and the value of the y-intercept?

In a test for the slope of the regression line being equal to zero versus the two-sided alternate, what is the value of the test statistic and the p-value?

A newspaper publisher is considering launching a new "national" newspaper in Anytown. It is believed that the newspaper would have to capture over 12% of the market in order to be financially viable. During the planning stages of this newspaper, a market survey was conducted of a sample of 400 readers. After providing a brief description of the proposed newspaper, one question asked if the survey participant would subscribe to the newspaper if the cost did not exceed $20 per month. Suppose that 58 participants said they would subscribe. a. Can the publisher conclude that the proposed newspaper will be financially viable? Perform the appropriate test at a 1% level of significance. b. Suppose the actual value of the overall proportion of readers who would subscribe to this newspaper is 0.13. Was the decision made in part (a) correct? If not, what type of error was made? c. State the meaning of a Type I and Type II error in the context of this scenario. And what would be the repercussions of making these errors to the publisher?

Going back to problem 1, in real life you can, without much difficulty, get the mean grade of Prof. Lax’s classes but that is about it; meaning you will have no idea how his grades would be distributed, nor would you have any idea about the standard deviation of these grades. (I doubt Prof. Lax would advertise his laxness on his website. Contrary what you might believe that is academically bad form and might negatively affect his students’ hireability in the job market). However, you have access to Miss Z’s data (which she swears is obtained by a random selection process) and the grades she obtained in her random sample of nine were: 79, 75, 84, 63, 98, 52, 87, 99, 83 a. To help Miss Z with her decision to take this course with Prof. Lax or not, create a 97% confidence interval (CI) for the mean using Miss Z.’s data. Make sure that you do the necessary checks. b. Does your interval capture the rumored population mean of 85? c. Calculate the margin of error (ME or simply E) of your confidence interval. d. Miss Z thinks a margin of error (or E) of 7 points or more will have a significant negative effect on her GPA. How does the ME (or E) of your 97% CI from part (c) compare to what she says her GPA can afford? If your CI’s ME (or E) is different than 7 points she can afford what are the ways you can use to reduce the margin of error down to 7 or smaller. Discuss all that can be done.

In a March 26-28, 2010 Gallup poll, 473 respondents (out of 1033) approved of they way President Obama handled the health care debate (regardless of their opinions on health care policy).

a) What is your point estimate for this proportion?

b) Construct a 95% confidence interval for this opinion. did a significant majority disapprove of how he handled the debate?

A company would like to estimate its total cost equation. It has collected 48 months of monthly production output and corresponding total production costs.  The collected data is in the file Production Cost Data Only.xlsx. Recall that

TOTAL COST = Fixed Costs + Variable Cost per Unit *Output.

Use the data to estimate a function that describes total cost for this company. (Round answers to 2 decimal places)

Develop a scatterplot of the two variables: monthly output and monthly total costs. Describe the relationship.

Estimate a total cost curve for this company.  State the estimated total cost function.

Based on your estimated total cost curve what is the estimated Fixed Cost for the Company?

Based on your estimated total cost curve what is the estimated average unit variable cost for the Company?

Develop a 95% confidence interval for the true average variable cost per unit.

What percent of the variation in monthly production costs is “explained” by the monthly production output?

Suppose the plant manager is interested in mean costs for several monthswhere output averages 30,000 units (i.e., Xp = 30). What is the predicted monthly total costs when output averages 30?  Construct a 95% confidence interval for the mean production costs for months that average 30,000 units of output.

We are to distribute 10 colored balls into five containers. Do the following:

1. Compute the probability of having at least one ball in each bucket if the balls are all different and the buckets are all labeled differently.

2. Compute the probability of having at least one ball in each bucket if the balls are all different and the buckets are all gray.

3. Compute the probability of having at least one ball in each bucket if the balls are gray and the buckets are all labeled differently.

4. Which one gives the most likelihood?

You are curious about the role of graduate status on work-life balance in Tech students. In a sample of 100 undergraduate students, 37 reported having trouble balancing school and work. In a separate sample of 75 graduate students, 50 had trouble with this balance. Test the null hypothesis that undergraduate or graduate students are equally likely to have trouble with work-life balance (alpha=0.05).

For independent sample t-tests: mean values for each sample, the variances for each sample, estimated standard error of the difference in means, the t-ratio, degrees of freedom, the t-critical value, and your decision to reject or retain the null.

For dependent sample t-tests: mean values for each sample, standard deviation for the difference between groups, standard error of the difference between the means, the t-ratio, degrees of freedom, the t-critical value, and your decision to reject or retain the null.

For proportions: sample proportions, combined proportions, standard error of the difference, z-score, critical z-score, and your decision to reject or retain the null.

Thirty small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 45.1 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit:

upper limit:

margin of error:

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit:

upper limit:

margin of error:

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit:

upper limit:

margin of error:

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error increases.

As the confidence level increases, the margin of error remains the same.

As the confidence level increases, the margin of error decreases.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval decreases in length.

As the confidence level increases, the confidence interval remains the same length.

As the confidence level increases, the confidence interval increases in length.

Consider the Nomad Machine Company (NMC) problem from class. As the problem stated: "you should develop two flow models" because NMC has sought "to build a new factory to expand its production capacity". Your task was to determine which factory to recommend.

In this discussion assignment, upload the JPG outcome for the optimal solution. Your uploaded solution should have a similar 'look and feel' professionalism as the JPG file on the external site (figure TP-F8). Make sure to use solver so the pink cells are populated. Also, using this optimal site selection, provide the operating costs for Cincinnati, Kansas City, and Pittsburgh.

A student group believes that less than 50% of students find their college experience extremely rewarding. They decide to test this hypothesis using a significance level of .05. They conduct a random sample of 100 students and 34 say they find their college experience extremely rewarding.

Based on the type of test this is (right, left, or two-tailed); determine the following for this problem.

4. Critical Value(s): _______________________

5. P-value Table A.3 _______________________ P-value Calculator:________________

P-value Table A.2 _______________

6: Can you reject? _______________________

7. Conclusion: Can we conclude or can we not conclude less than 50% of students find their college experience extremely rewarding? (write the conclusion in a sentence)

A survey found that​ women's heights are normally distributed with mean 62.3 in. and standard deviation 3.6 in. The survey also found that​ men's heights are normally distributed with mean 67.7 in. and standard deviation 3.3 in. Consider an executive jet that seats six with a doorway height of 55.7 in. Complete parts​ (a) through​ (c) below.

a. What percentage of adult men can fit through the door without​ bending?

The percentage of men who can fit without bending is

___.

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

b. Does the door design with a height of

55.755.7

in. appear to be​ adequate? Why​ didn't the engineers design a larger​ door?

A.

The door design is​ inadequate, but because the jet is relatively small and seats only six​ people, a much higher door would require major changes in the design and cost of the​ jet, making a larger height not practical.

B.

The door design is​ adequate, because the majority of people will be able to fit without bending.​ Thus, a larger door is not needed.

C.

The door design is​ adequate, because although many men will not be able to fit without​ bending, most women will be able to fit without bending.​ Thus, a larger door is not needed.

D.

The door design is​ inadequate, because every person needs to be able to get into the aircraft without bending. There is no reason why this should not be implemented.

c. What doorway height would allow​ 40% of men to fit without​ bending?

The doorway height that would allow​ 40% of men to fit without bending is

__

in.

​(Round to one decimal place as​ needed.)

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6950 and estimated standard deviation σ = 2650. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. (a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.) (b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? The probability distribution of x is not normal. The probability distribution of x is approximately normal with μx = 6950 and σx = 1873.83. The probability distribution of x is approximately normal with μx = 6950 and σx = 1325.00. The probability distribution of x is approximately normal with μx = 6950 and σx = 2650. What is the probability of x < 3500? (Round your answer to four decimal places.) (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) (d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased? The probabilities decreased as n increased. The probabilities stayed the same as n increased. The probabilities increased as n increased. If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse? It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia. It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia. It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia. It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

The mass of plants in a botany lab are normally distributed with a mean of 54 grams and a standard deviation of 6.5 grams. Use this to compute : a. The probability that one randomly chosen plant will have a mass that less than 49.25 grams b. The probability that one randomly chosen plant will have a mass that is between 52 grams and 62 grams. c. The mass of a plant which weighs less than the top 15% of plants in the lab. d. The probability that 25 randomly chosen plants will have a mean mass of no more than 50 grams

What is the critical F value when the sample size for the numerator is sixteen and the sample size for the denominator is ten? Use a two-tailed test and the 0.02 significance level. (Round your answer to 2 decimal places.)

An evaluation was recently performed on brands and data were collected that classified each brand as being in the technology or financial institutions sector and also reported the brand value. The results in terms of value​ (in millions of​ dollars) are shown in the accompanying data table. Complete parts​ (a) through​ (c).

BRAND VALUES:

Technology: 281, 377, 491, 429, 406, 584, 641, 624

Financial Institutions: 517, 832, 819, 804, 937, 995, 1035, 1094

a.)

Assuming the population variances are​ equal, is there evidence that the mean brand value is different for the technology sector than for the financial institutions​ sector? (Use α=0.05​.)

Determine the hypotheses. Let μ1 be the mean brand value for the technology sector and μ2 be the mean brand value for the financial institutions sector. Choose the correct answer below.

A.) H0: μ1= μ2

H1: μ1≠μ2

B.) H0: μ1≤ μ2

H1: μ1 > μ2

C.) H0: μ1≥ μ2

H1: μ1< μ2

D.) H0: μ1≠μ2

H1: μ1=μ2

-Find the test statistic.

^tSTAT=___

-Choose the correct answer below.

A. Reject H0. There is sufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

B. Reject H0. There is insufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

C. Do not reject H0. There is sufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

D.Do not reject H0. There is insufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

b.)

-Repeat​ (a), assuming that the population variances are not equal.

A.) H0: μ1= μ2

H1: μ1≠μ2

B.) H0: μ1≤ μ2

H1: μ1 > μ2

C.) H0: μ1≥ μ2

H1: μ1< μ2

D.) H0: μ1≠μ2

H1: μ1=μ2

-FInd the test statistic.

^tSTAT=____

-Choose the correct answer below.

A. Reject H0. There is sufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

B. Reject H0. There is insufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

C. Do not reject H0. There is sufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

D.Do not reject H0. There is insufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

c.)

-Compare the results of (a) and (b).

A. The conclusions for parts​ (a) and​ (b) are different. Reject the null hypothesis in​ (b) and do not reject it in​ (a).

B.The conclusions for parts​ (a) and​ (b) both reject the null hypothesis.

C.The conclusions for parts​ (a) and​ (b) both do not reject the null hypothesis.

D. The conclusions for parts​ (a) and​ (b) are different. Reject the null hypothesis in​ (a) and do not reject it in​ (b).