The temperature at a point (x,y,z) is given by T(x,y,z)=200e^(-x^2-y^2/4-z^2/9) , where T is measured in degrees Celsius and x,y, and z in meters. just try to keep track of what needs to be a unit vector. a) Find the rate of change of the temperature at the point (1, 1, -1) in the direction toward the point (-5, -4, -3). b) In which direction (unit vector) does the temperature increase the fastest at (1, 1, -1)? c) What is the maximum rate of increase of T at (1, 1, -1)?

Data on 72 randomly selected flights departing from the three major NYC airports. Departure in minutes. Negative times represent early departures.

Q. NYC airport management claim that the average departure delay times for flights that departed from major NYC airports in 2013 is less than 15 minutes. Test the claim at the 1% level of significance using the critical value approach. Show all working. (Hint: you need to obtain the sample statistics required from the data and state all values to two decimal places)

(a) We now wish to test if more than 30% of flights that departed from the NYC airports in 2013 are delayed. Use a p-value approach at the 10% level of significance. Show all working. (Hints: you need to obtain the sample statistic using the data and keep the value to three decimal places)

(b) Define a Type I error and explain it in the context of the hypothesis test in (a).

Using the information provided in the following​ table, find the value of each​ asset:

The value of Asset A is ​

The value of Asset B

The value of Asset C

The value of Asset D

The value of Asset E

Is there a fourth degree polynomial that takes these values?

Rao Technologies, a California-based high-tech manufacturer, is considering outsourcing some of its electronics production. Four firms have responded to its request for bids, and CEO Mohan Rao has started to perform an analysis on the scores his OM team has entered in the table below. RATINGS OF OUTSOURCE PROVIDERS FACTOR WEIGHT A B C D Labor w 5 4 3 5 Quality procedures 30 2 3 5 1 Logistics system 5 3 4 3 5 Price 25 5 3 4 4 Trustworthiness 5 3 2 3 5 Technology in place 15 2 5 4 4 Management team 15 5 4 2 1 Weights are on a scale from 1 through 30, and the outsourcing provider scores are on a scale of 1 through 5. The weight for the labor factor is shown as a w because Rao’s OM team cannot agree on a value for this weight. For what range of values of w, if any, is company C a recommended outsourcing provider, according to the factor-rating method? Please show work. Thank you

Use the following time-series data to answer the given questions. Time Period Value 1 27 2 30 3 58 4 63 5 59 6 67 7 70 8 86 9 101 10 97 a. Develop forecasts for periods 5 through 10 using 4-month moving averages. b. Develop forecasts for periods 5 through 10 using 4-month weighted moving averages. Weight the most recent month by a factor of 4, the previous month by 2, and the other months by 1. c. Compute the errors of the forecasts in parts (a) and (b) and observe the differences in the errors forecast by the two different techniques. (Round your answers to 3 decimal places.) a. Time Period Value 4-Month Moving Average Forecast 1 27 - 2 30 - 3 58 - 4 63 - 5 59 6 67 7 70 8 86 9 101 10 97 b. Time Period Value 4-Month Weighted Moving Average Forecast 1 27 - 2 30 - 3 58 - 4 63 - 5 59 6 67 7 70 8 86 9 101 10 97 c. Time Period Value Forecast Error, 4-Month Moving Average Forecast Error, 4-Month Weighted Moving Average Differences in error 1 27 - - - 2 30 - - - 3 58 - - - 4 63 - - - 5 59 6 67 7 70 8 86 9 101 10 97 In each time period, the four-month moving average produces errors of forecast than the four-month weighted moving average.

Technician           Technician

1                              2

1.45                        1.54

1.37                       1.41

1.21                        1.56

1.54                        1.37

1.48                        1.2

1.29                        1.31

1.34                        1.27

1.35

Two quality control technicians measured the surface finish of a metal part, obtaining the data in the table below. Assume that the measurements are normally distributed.

a. Test the hypothesis that the mean surface finish measurements made by the two technicians are equal. Use α = 0.05 and assume equal variances. b. What are the practical implications of the test in part (a)? Discuss what practical conclusions you would draw if the null hypothesis were rejected. c. Assuming that the variances are equal, construct a 95% confidence interval on the mean difference in surface-finish measurements d. Test the hypothesis that the variances of the measurements made by the two technicians are equal. Use α = 0.05. What are the practical implications if the null hypothesis is rejected? e. Construct a 95% confidence interval estimate of the ratio of the variances of technician measurement error.Please solve urgent

Technician           Technician

1                              2

1.45                        1.54

1.37                       1.41

1.21                        1.56

1.54                        1.37

1.48                        1.2

1.29                        1.31

1.34                        1.27

1.35

Two quality control technicians measured the surface finish of a metal part, obtaining the data in the table below. Assume that the measurements are normally distributed.

a. Test the hypothesis that the mean surface finish measurements made by the two technicians are equal. Use α = 0.05 and assume equal variances. b. What are the practical implications of the test in part (a)? Discuss what practical conclusions you would draw if the null hypothesis were rejected. c. Assuming that the variances are equal, construct a 95% confidence interval on the mean difference in surface-finish measurements d. Test the hypothesis that the variances of the measurements made by the two technicians are equal. Use α = 0.05. What are the practical implications if the null hypothesis is rejected? e. Construct a 95% confidence interval estimate of the ratio of the variances of technician measurement error.

Sample 1:                    {2,4,3,6,7,9,8}

Sample 2:                    {3,7,4,5,9}

1. Test the hypothesis that the population from which the Sample 1 was drawn has a mean that is no more than 7.
2. Test the hypothesis that the population from which the Sample 2 was drawn has a mean that is no more than 5.
3. Test the hypothesis that the population from which the Sample 1 was drawn has a variance that is no more than 10.
4. Test the hypothesis that the population from which the Sample 1 was drawn has a variance that is at least 8.
5. Test the hypothesis that the population from which the Sample 2 was drawn has a variance that is no more than 6.
6. Test the hypothesis that the population from which the Sample 2 was drawn has a variance that is at least 7.
7. Test the hypothesis that the population from which the Sample 1 was drawn has a mean that is at least 5.
8. Test the hypothesis that the population from which the Sample 2 was drawn has a mean that is at least 6.
9. Test the hypothesis that the variances of the two populations from which these two samples were drawn are equal to each other.
10. Test the hypothesis that the population from which the Sample 1 was drawn has a mean that is 2 units more than the population from which the Sample 2 was drawn.

Sample 1:                    {2,4,3,6,7,9,8}

Sample 2:                    {3,7,4,5,9}

1. Find the mean, median, variance, standard deviation, skewness, minimum, maximum, range, and 95% confidence interval of the population mean for each of the samples.
2. Construct the 95% confidence interval of the difference of the two population means from which these two samples were drawn.
3. Test the hypothesis that the population from which the Sample 1 was drawn has a mean that is no more than 7.
4. Test the hypothesis that the population from which the Sample 2 was drawn has a mean that is no more than 5.
5. Test the hypothesis that the population from which the Sample 1 was drawn has a variance that is no more than 10.
6. Test the hypothesis that the population from which the Sample 1 was drawn has a variance that is at least 8.
7. Test the hypothesis that the population from which the Sample 2 was drawn has a variance that is no more than 6.
8. Test the hypothesis that the population from which the Sample 2 was drawn has a variance that is at least 7.
9. Test the hypothesis that the population from which the Sample 1 was drawn has a mean that is at least 5.
10. Test the hypothesis that the population from which the Sample 2 was drawn has a mean that is at least 6.
11. Test the hypothesis that the variances of the two populations from which these two samples were drawn are equal to each other.
12. Test the hypothesis that the population from which the Sample 1 was drawn has a mean that is 2 units more than the population from which the Sample 2 was drawn.
13. Looking at your answers to questions above, what can you say about the (potentially) two populations from which these two samples were drawn? What do you think about the likelihood that these two samples were in fact drawn from the same population? Provide detailed justification for your answer.