Ten females were divided into two equal groups. One group was taught how to concentrate on their breathing (a breathing meditation). A second group was told to imagine that the day was very hot and that they would be allowed to place their hand in cool water. Both groups placed their right hand in buckets of ice water for three minutes. Afterward, they rated their pain on a scale of one to seven (with seven meaning intense pain). Analyze the data and conclude whether the any of the methods was effective in reducing pain.

A. What is the dependent variable?
B. What is the null and alternate hypothesis?
C. Calculate t and note the critical values
D. Calculate d
E. Write your results and interpretations with appropriate stat notations.

Breathing Meditation       Imagination

                             3                         4

                             2                         5

                             4                         7

                             3                         6

                             2                         6

At a certain coffee​ shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 330 cups and a standard deviation of 23 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 170 doughnuts and a standard deviation of 13. Complete parts​ a) through​ c).

Question: The shop is open every day but Sunday. Assuming​ day-to-day sales are​ independent, what's the probability​ he'll sell over 2000 cups of coffee in a​ week? _____________ (round to three decimals as needed.)

Question: Whats the probability that on any given day he'll sell a doughnut to more than half of his coffee customers ? ___________ (round to three decimal places as needed).

A. The data below represent a random sample of 9 scores on a statistics quiz. (The maximum possible score on the quiz is 10.) Assume that the scores are normally distributed with a standard deviation of 1.6. Estimate the population mean with 93% confidence. 6,10,6,4,5,7,2,9,6 6 , 10 , 6 , 4 , 5 , 7 , 2 , 9 , 6 Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

B. Among the most exciting aspects of a university professor's life are the departmental meetings where such critical issues as the color the walls will be painted and who gets a new desk are decided. A sample of 20 professors was asked how many hours per year are devoted to such meetings. The responses are listed below. Assuming that the variable is normally distributed with a standard deviation of 6 hours, estimate the mean number of hours spent at departmental meetings by all professors. Use a confidence level of 90%.

7,11,11,10,17,5,4,9,19,14,4,1,22,10,15,21,17,3,18,16

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

The daily exchange rates for the​ five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.814 in currency A​ (to currency​ B) and standard deviation 0.035 in currency A. Given this​ model, and using the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more​ precisely, complete parts​ (a) through​ (d).

Question: ​a) What would the cutoff rate be that would separate the highest 2.5​% of currency​ A/currency B​ rates? The cutoff rate would be ___________ (type an integer or a decimal rounded to the nearest thousandth as needed)

Question: What would the cutoff rate be that would separate the highest 50% ? The cutoff rate would be _______________

Question: What would the cutoff rate be that would separate the middle 68% ? The lower cutoff rate would be ____________

Question: The upper cutoff rate would be ? ____________________

Question: What would the cutoff rate be that would separate the highest 16%? ________________

A building contractor buys 80% of his cement from supplier A and 20​% from supplier B. A total of 75​% of the bags from A arrive​ undamaged, while 85​% of the bags from B arrive undamaged. Find the probability that a damaged bag is from supplier Upper A.

It is common wisdom that death of a spouse can lead to health deterioration of the partner left behind. Is common wisdom right or wrong in this case? To investigate, Maddison and Viola (1968) measured the degree of health deterioration of 132 widows in the Boston area, all of whose husbands had died at the age of 45-60 within a fixed six-month period before the study. A total of 28 of the 132 widows had experienced a marked deterioration in health, 47 had seen a moderate deterioration, and 57 had seen no deterioration in health.Of 98 control women with similar characteristics who had not lost their husbands, 7 saw a marked deterioration in health over the same time period, 31 experienced a moderate deterioration of health, and 60 saw no deterioration.

1) Is this study observational or experimental?

2) State the null and alternative hypothesis

3) Which appropriate statistical test would be done for this experiment? Contingency analysis, t-test or goodness of fit?

The owner of a local golf course wants to examine the difference between the average ages of males and females that play on the golf course. Specifically, he wants to test if the average age of males is greater than the average age of females. If the owner conducts a hypothesis test for two independent samples and calculates a p-value of 0.5441, what is the appropriate conclusion? Label males as group 1 and females as group 2.

You are looking for a way to incentivize the sales reps that you are in charge of. You design an incentive plan as a way to help increase in their sales. To evaluate this innovative plan, you take a random sample of your reps, and their weekly incomes before and after the plan were recorded. You calculate the difference in income as (after incentive plan - before incentive plan). You perform a paired samples t-test with the following hypotheses: Null Hypothesis: μ_D ≥ 0, Alternative Hypothesis: μ_D< 0. You calculate a p-value of 0.001. What is the appropriate conclusion of your test?

It is reported in USA Today that the average flight cost nationwide is $468. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually different from $468. The hypotheses for this situation are as follows: Null Hypothesis: μ = 468, Alternative Hypothesis: μ ≠ 468. If the true average flight cost nationwide is $468 and the null hypothesis is rejected, did a type I, type II, or no error occur?

1. a There is a 50% chance of thunderstorms on Monday, a 50% chance on Tuesday and a 50% chance on Wednesday. Assume these are independent events. What is the probability that there will be thunderstorms on Monday, Tuesday, and Wednesday? Show your work.   b) A student says that if P(A) = P(A|B), then A and B must be independent events. Is the student correct? Explain.  Give a real life example that can be represented by P(A) = P(A|B). c) Describe the relationship between a change in the sample size and the chance in the margin of error.d) Describe a situation with a 20% probability of success in each of 4 trials. Graph the binomial distribution. e) On a math test the mean score is 82 with a standard deviation of 3. A passing score is 70 or greater. Choose a passing score that you would consider to be the outlier. Justify your choice.

1)Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. Round to two decimal places. α = 0.07; alternate hypothesis H 1 is μ ≠ 3.24 LaTeX: \pm ± __________

2)Use the given information to find the P-value. The test statistic in a right-tailed test is z = 0.21. Round to two decimals.

3)Find the P-value for the indicated hypothesis test. A medical school claims that more than 14% of its students plan to go into general practice. It is found that among a random sample of 99 of the school's students, 25% of them plan to go into general practice. Find the P-value for a test of the school's claim. Round to 4 decimals.

5)Find the P-value for the indicated hypothesis test. An airline claims that the no-show rate for passengers booked on its flights is less than 5%. Of 380 randomly selected reservations, 18 were no-shows. Find the P-value for a test of the airline's claim. Round to 2 decimals.

. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 25 metal sheets are given below. Use the simple linear regression model. ∑X = 50 ∑X2 = 200 ∑Y = 75 ∑Y2 = 1600 ∑XY = 400 Find the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 4 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination. Test the significance of the slope.

The city of Bloomington is about to build a new water treatment plant. Once the plant is designed (D) we can select the site (S), the building contractor (C and the operating personnel (P). Once the site is selected we may erect the building (B). We can order the water treatment machine (W) and prepare the operations manual (M) only after the contractor is selected. We can begin training the operators (T) when both the operations manual and operating personnel selected are completed.  When the water treatment and building are finished, we can install the treatment machine (I). Once the treatment machine is installed and the operators are trained, we can obtain an operating license (L). The time to complete each activity is assumed to be a normal distribution and the estimated mean and standard deviation of the time (in months) needed to complete each activity is defined below:

1. Draw the PERT network for the project
2. Calculate the critical path and estimated completion time of the project
3. Using this estimated completion time, determine the probability of completing the project in (1) under 50 months and (2) over 55 months
4. Use simulation to calculate the estimated completion time and to determine the probability of completing the project in (1) under 50 months and (2) over 55 months (use a monte carlo simulation of 200 repetitions)
5. Explain why the answers to questions (b) and (c ) may differ to that determined in question (d).
6. Use simulation to estimate the probability that B, I and T are critical activities

The file P02_35.xlsx contains data from a survey of 500 randomly selected households. a. Suppose you decide to generate a systematic random sample of size 25 from this population of data. How many such samples are there? What is the mean of Debt for each of the first three such samples, using the data in the order given? b. If you wanted to estimate the (supposedly unknown) population mean of Debt from a systematic random sample as in part a, why might it be a good idea to sort first on Debt? If you do so, what is the mean of Debt for each of the first three such samples? Please provide answer in Excel format with steps how to do it. I am not able to upload full table.

Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following (hypothetical) data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here): Brand Price (X) Score (Y) Dell 3800 50 Hisense 2800 45 Hitachi 2700 35 JVC 3000 40 LG 3500 45 Maxent 2000 28 Panasonic 4000 57 Phillips 3200 48 Proview 2000 22 Samsung 3000 30 Use the above data to develop and estimated regression equation. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3600. Perform test of significance for slope coefficient.

1.             Develop a simple linear regression model to predict the price of a house based upon the living area (square feet) using a 95% level of confidence.

1.             Write the reqression equation
2.             Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.
3.              Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.
4.             Interpret the coefficient for the independent variable.
5.             What percentage of the observed variation in housing prices is explained by the model?
6.              Predict the value of a house with 3,000 square feet of living area.

2.             Develop a simple linear regression model to predict the price of a house based upon the number of bedrooms using a 95% level of confidence.

1.             Write the reqression equation
2.             Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.
3.              Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.
4.             Interpret the coefficient for the independent variable.
5.             What percentage of the observed variation in housing prices is explained by the model?
6.              Predict the value of a house with 3 bedrooms.

3.             Develop a simple linear regression model to predict the price of a house based upon the number of bathrooms using a 95% level of confidence.

1.             Write the reqression equation
2.             Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.
3.              Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.
4.             Interpret the coefficient for the independent variable.
5.             What percentage of the observed variation in housing prices is explained by the model?
6.              Predict the value of a house with 2.5 bathrooms.

4.             Develop a simple linear regression model to predict the price of a house based upon its age using a 95% level of confidence.

1.             Write the reqression equation
2.             Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.
3.              Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.
4.             Interpret the coefficient for the independent variable.
5.             What percentage of the observed variation in housing prices is explained by the model?
6.              Predict the value of a house that is 50 years old.

5.             Compare the preceding four simple linear regression models to determine which model is the preferred model. Use the Significance F values, p-values for independent variable coefficients, R-squared or Adjusted R-squared values (as appropriate), and standard errors to explain your selection.
6.             Calculate the predicted sale price of a 50 year old house with 3,000 square feet of living area, 3 bedrooms, and 2.5 bathrooms using your preferred regression model from part 5.

Prepare a single Microsoft Excel file, using a separate worksheet for each regression model, to document your regression analyses. Prepare a single Microsoft Word document that outlines your responses for each portions of the case study.

Selling Price        Age (Years)         Living Area (Sq Feet)       No. Bathrooms No Bedrooms

$92,000                 18           1,527     2              4

$211,002              0              2,195     2.5          4

$115,000              14           1,480     1.5          3

$113,000              53           1,452     2              3

$216,300              0              2,360     2.5          4

$145,000              32           1,440     1              3

$114,000              14           1,480     2.5          2

$139,050              125         1,879     2.5          3

$104,000              14           1,480     1.5          3

$169,900              11           1,792     2.5          3

$177,900              2              1,386     2.5          3

$133,000              14           1,676     2              2

$185,000              0              768         2              4

$115,000              16           1,560     1.5          3

$100,000              91           1,000     1              3

$117,000              15           1,676     1.5          4

$150,000              11           1,656     1.5          3

$187,500              11           2,300     1.5          3

$107,000              25           1,712     1              3

$126,900              26           1,350     1.5          3

$147,000              15           1,676     2.5          3

$62,000                 103         1,317     1.5          3

$101,000              30           1,056     2              3

$143,500              13           912         1              3

$113,400              18           1,232     2              2

$112,000              36           1,280     1              3

$112,500              43           1,232     1              3

$97,000                 45           1,406     1.5          3

$121,000              6              1,164     2              3

$65,720                 123         1,198     1              3

$225,000              10           2,206     2.5          4