Suppose that the lifetimes of light bulbs are approximately normally​ distributed, with a mean of

56 hours and a standard deviation of 3.3 hours. With this​ information, answer the following questions.​

(a) What proportion of light bulbs will last more than61 ​hours?

​(b) What proportion of light bulbs will last51 hours or​ less?​

(c) What proportion of light bulbs will last between59 and 62 hours?​

(d) What is the probability that a randomly selected light bulb lasts less than 45 ​hours?

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 5 years. (Y) Sales in Millions of Dollars 15 16 18 17 16 (X) Advertising in ($10,000) 32 33 35 34 36

(a) Compute the coefficient of determination for the estimated regression equation you got in the previous in-class problem.

(b) Interpret the meaning of the value of the coefficient of determination that you found in (a). Be very specific.

(c) Perform a t test and determine whether or not X and Y are related. Let = 0.05.

(d) Perform an F test and determine whether or not X and Y are related. Let = 0.05.

Paint-Drying Robots. How long it takes paint to dry can have an impact on the production capacity of a business. In May 2018, Deal’s Auto Body & Paint in Prescott, Arizona, invested in a paint­drying robot to speed up its process (The Daily Courier website, https://www.dcourier.com/photos/2018/may/26/984960336/). An interesting question is, “Do all paint­drying robots have the same drying time?” To test this, sup­ pose we sample five drying times for each of different brands of paint­drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained.
Robot 1: 128 137 135 124 141

Robot 2: 144 133 142 146 130
Robot 3 : 133 143 137 136 131
Robot 4: 150 142 135 140 153

At the a = .05 level of significance, test to see whether the mean drying time is the same for each brand of robot

Teleconferences, electronic mail, and word processors are among the tools that can
reduce the length of business meetings. A recent survey indicated that the percentage
reduction y in time spent by business professionals in meetings due to an automated office
equipment is approximately normally distributed with mean equal to 15% and standard
deviation equal to 4%.

a. what proportion of all business professionals with access to automated office equipment
have reduced their time in meetings by more than 22%

a. what proportion of all business professionals with access to automated office equipment
have reduced their time in meetings by 10 % or less?

From a group of three data-processing managers, two senior system analysts, and two quality control engineers, three people are to randomly selected to form a committee that will study the feasibility of adding computer graphics at a consulting firm. Let y1 denote the number of data-processing managers and y2 the number of senior systems analysts selected for the committee.

a. Determine whether y1 and y2 are independent
b. Find E(y1-2y2)
c. Find the covariance of the random variable y1 and y2.
d. Find the varianve of y1 and also the variance of y2
e. Find the correlation of the random variable y1 and y2
f. Find the covariance matrix of the random variable y1 and y2
g. Find the correlation matrix of the random variable y1 and y2

Research Scenario: A social psychologist is studying the differences in the number of Facebook® friends between identical twins raised apart. She believes that twins raised in different environments will have differences in the number of friends, which would help point to the influence of environmental factors over inherited factors on social outcomes. She divides the twins into two groups (“Twin 1” and “Twin 2”), collects the data and creates the table below.

Using this table, enter the data into a new SPSS data file and run a paired-samples t test to test the claim that the identical twins raised apart will have a different number of Facebook® friends. Follow the directions below the table to complete the homework.

1. Paste SPSS output. (7 pts)

2. Write an APA-style Results section based on your analysis. Include your boxplot as an APA-style figure as demonstrated in the APA writing presentation. (Results = 8 pts; Graph = 5 pts)

Question
Sampling is the process of selecting a representative subset of observations from a population to determine characteristics (i.e. the population parameters) of the random variable under study. Probability sampling includes all selection methods where the observations to be included in a sample have been selected on a purely random basis from the population. Briefly explain FIVE (5) types of probability sampling

The weight of a car can influence the mileage that the car can obtain. A random sample of 20 cars’ weights and mileage is collected. The table for the weight and mileage of the cars is given below. Use Excel to find the best fit linear regression equation, where weight is the explanatory variable. Round the slope and intercept to three decimal places.

Weight   Mileage
30.0   32.2
20.0   56.0
20.0   46.2
45.0   19.5
40.0   23.6
45.0   16.7
25.0   42.2
55.0   13.2
17.5   65.4
35.0   28.0
27.5   49.9
27.5   35.1
30.0   31.2
25.0   29.5
40.0   25.6
22.5   43.4
35.0   28.9
27.5   35.0
22.5   38.8
45.0   17.2

(a) In the Monty Hall problem with 100 doors, you pick one and Monty opens 98 other doors with goats. What is the probability of winning (assuming you would rather have a car than a goat) if you switch to the remaining door? Explain your answer.

(b) Suppose Monte opens 98 doors without checking for cars. What is the probability that, once the doors are open, changing your choice will not change your chances of winning.

How would you describe descriptive, predictive, and prescriptive data analytics? What options do we have for data analytic tools? Which option is the best for big data analysis in your opinion and why?

Your initial posting should be 250-500 words

An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the color index, or B−V index, and distance (in light years) from Earth for 30 stars. The color index of a star is the difference in the light absorption measured from the star using two different light filters (a B and a V filter). This then allows the scientist to know the star's temperature and a negative value means a hot blue star. A light year is the distance light can travel in 1 year, which is approximately 5.9 trillion miles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places.

B-V index   Distance (ly)
1.1   1380
0.4   556
1.0   771
0.5   304
1.4   532
1.0   751
0.5   267
0.8   229
0.5   552
0.2   896
1.5   1819
0.5   381
0.5   257
1.1   541
0.7   133
0.5   300
0.0   985
0.4   525
1.0   408
1.1   1367
1.07   2848
1.1   128.9
1.12   1766.2
0.64   186.5
0.87   8269.2
0.19   828.9
1.03   153
0.55   223.6
1.39   963.9
0.89   91.7

In a sample of 808 Republicans, 380 answered that they believe that Sarah Palin has the right experience to be President. Assuming the polling was done correctly and that the data is current, is it reasonable to conclude at a significance level of .01 that less than fifty percent of Republicans feel that Sarah Palin has the right experience to be President?

State the following:

1. sample size

2. sample proportion to three decimal places

3. what type of variable is it?

4. The data is collected from an SRS. Is the sample size sufficiently large?

5. state the null hypothesis.

6. state the alternate hypothesis.

7. write the formula for the standard error and compute it to four decimal places.

8. write the formula for the z-value (test statistic) and compute it to two decimal places.

9. critical value(s)

10. p-value table A3

11. p-value table A2

12. p-value calculator

13. can we reject?

14. conclusion

15. (same problem as above but the level of significance is .05 instead of .01) critical value (s)

15b. conclusion with .05 level

hirty-five cities provided information on vacancy rates (in percent) for local apartments in the following frequency distribution. Vacancy Rate (in percent) Frequency 0 up to 3 7 3 up to 6 5 6 up to 9 6 9 up to 12 8 12 up to 15 9 a. Calculate the average vacancy rate. (Round your answer to 4 decimal places.) b. Calculate the variance and the standard deviation for this sample. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Biased coin has Q as unknows bias. Q is uniform continuos random variable ranges from 0 to t ( 0 < t <= 1). t is a constant.

N = Number of toss using the biased coin till we get the first head.

Find expectation of Q divided by LMS estimator of Q

i.e. What is E [ Q / LMS of (Q) ] ?

According to the Environmental Protection Agency (EPA), the 2018 Toyota Camry L drives an average of 420.5 miles on a full tank of gas. Assume the mileage follows a normal distribution with a standard deviation of 50 miles. Answer the following questions:

17.) Determine the number of miles that the car will travel with 90%, 30%, and 50% probability on a full tank of gas.

18.) Determine the UPPER AND LOWER value(s) for the interval of miles traveled on a full tank of gas around the mean that includes approximately 68% of miles for this car.

19.) Determine the UPPER AND LOWER value(s) for the interval of miles traveled on a full tank of gas around the mean that includes approximately 95% of miles for this car.

20.) Determine the UPPER AND LOWER value(s) for the interval of miles traveled on a full tank of gas around the mean that includes approximately 99.7% of miles for this car.