For the following situations, please write out null and alternative hypotheses.

a. Assuming m = 100, do children who watch more than three hours of TV per day have significantly lower IQs?

b. Assuming m = 100, a cognitive psychologist would like to know if the IQs of children who play outside at least three days a week are different from that of the population.

c. Assuming m = 50, write out the null and a non-directional alternative hypothesis.

identify (but don't collect) a type of dataset that might be normally distributed, and then answer the following questions:

• What is brief description of the data?
• Is the data normally distributed? Specifically, why is the data not uniformly distributed, or distributed in some other way?
• Normal data is clustered around the mean; what might cause the data you identified to have a different shape and not be clustered around the mean?

A simple random sample of 60 items from a population of with α=8 resulted in a sample mean of 35.

A. Provide a 90% confidence interval for the population mean.

B. Provide a 95% confidence interval for the population mean.

C. Provide a 99% confidence interval for the population mean.

Round to 2 decimal places if necessary.

The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these​ data, the​ least-squares regression line is ModifyingAbove y with -0.006x + 42.216. A twelfth car weighs 3,425 pounds and gets 12 miles per gallon.

​(a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on Rsquared​? ​

(b) Is the point corresponding to the twelfth car​ influential? Is it an​ outlier?

Car, Weight (pounds) x, Miles per Gallon y
1 3766 20
2 3989 21
3 3532 20
4 3170 22
5 2575 28
6 3735 20
7 2605 27
8 3772 18
9 3310 19
10 2993 26
11 2755 25

A point is chosen uniformly at random from a disk of radius 1, centered at the origin. Let R be the distance of the point from the origin, and Θ the angle, measured in radians, counterclockwise with respect to the x-axis, of the line connecting the origin to the point.

1. Find the joint distribution function of (R,Θ); i.e. find F(r,θ) = P(R ≤ r, Θ ≤ θ).

2. Are R and Θ independent? Explain your answer.

In the Blade Runner universe, replicants are bioengineered androids that are virtually identical to humans. The “Voight-Kampff” test is designed to distinguish replicants from humans based on their emotional response to test questions. The test designers guarantee an accuracy rate of 90%. In other words, they guarantee that if a replicant is subjected to the test, then the test will correctly label them as a replicant with probability q = 90%. With the remaining probability, the test incorrectly labels the replicant as a human. Similarly, if a human is subjected to the test, then they will be correctly labelled as human with probability q = 90%, and with the remaining probability they will be incorrectly labelled as a replicant. A subject, Leon, is suspected to be a replicant. Your prior probability that Leon is a replicant equals p = 75% and with the remaining probability 1 − p = 25% you suspect Leon is a human. (a) What is the probability that if Leon takes the Voight-Kampff test, the test will label him as a replicant? (b) Leon is subjected to the Voight-Kampff test, and the test labels Leon as a replicant. What is your posterior probability about whether Leon is a replicant or not? (c) Another subject, Deckard, is also suspected to be a replicant, and your prior probability is that Deckard is a replicant with probability p1 = 10% and human with probability 1 − p1 = 90%. Deckard takes the test, and is labelled as a human. What is your posterior probability about Deckard?

. Arsalaan A., a well-known financial analyst, selected 50 consecutive years of U.S. financial markets data at random. For 11 of the years, the rate of return for the Dow Jones Industrial Average [DJIA] exceeded the rates of return for both the S&P 500 Index and the NASDAQ Composite Index. For 8 of the years, the rate of return for the DJIA trailed the rates of return for both the S&P 500 and the NASDAQ. For 21 of the years, the rate of return for the DJIA trailed the rate of return for the S&P 500. Over the 50 years,

a. determine the probability the rate of return for the DJIA trailed the rate of return for the NASDAQ.
b. determine the probability the rate of return for the DJIA trailed the rate of return for at least one of the other two Indexes.
c. determine the probability the rate of return for the DJIA trailed the rate of return for the S&P 500 given it trailed the rate of return for the NASDAQ.
d. determine the probability the rate of return for the DJIA exceeded the rate of return for the S&P 500 given it exceeded the rate of return for the NASDAQ.

A psychologist is interested in constructing a 95% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 74 of the 715 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible. a. With 95% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between and . b. If many groups of 715 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about percent will not contain the true population proportion.

What approaches are there by which coefficients are estimated for linear and logistic regression?

How is the deviance affected when an explanatory term is omitted (i know that it increases, but surely there is more to it?)

In what situations would we use Beta-binomial regression?

Please discuss the purpose of hypothesis testing. In your response, provide an example of a null hypothesis and alternative hypothesis. Why is hypothesis testing important for researchers?

Note: The response needs to be at a minimum of 350 words typed please.

1. Calculate the weekly return for BIT and construct a histogram in Excel. Does the data on return rates appear normally distributed? On the basis of z-scores do you find evidence of outliers? Hint: the formula for a return is (Current Price – Previous price)/Previous price multiplied by 100.

2. Date	BIT
   11/3/13	52.06
   18/3/13	53.84
   25/3/13	99.99
   1/4/13	139.23
   8/4/13	113.07
   15/4/13	123.93
   22/4/13	141.36
   29/4/13	126.5
   6/5/13	120.39
   13/5/13	125.5
   20/5/13	142.52
   27/5/13	137.88
   3/6/13	115.66
   10/6/13	120.98
   17/6/13	125.28
   24/6/13	111.97
   1/7/13	97.54
   8/7/13	114.95
   15/7/13	96.5
   22/7/13	92
   29/7/13	99.95
   5/8/13	125.49
   12/8/13	104.1
   19/8/13	109.53
   26/8/13	158.75
   2/9/13	136.12
   9/9/13	147.87
   16/9/13	143.09
   23/9/13	142.08
   30/9/13	140.24
   7/10/13	151.77
   14/10/13	193.52
   21/10/13	213.89
   28/10/13	233.5
   4/11/13	331.05
   11/11/13	547.08
   18/11/13	974.55
   25/11/13	1191.99
   2/12/13	1016.27
   9/12/13	1027.82
   16/12/13	781.78
   23/12/13	889.11
   30/12/13	999
   6/1/14	1037.92
   13/1/14	977.1
   20/1/14	1000
   27/1/14	928.99
   3/2/14	850
   10/2/14	740
   17/2/14	728.37
   24/2/14	650
   3/3/14	674.73
   10/3/14	669.53
   17/3/14	646.83
   24/3/14	560
   31/3/14	518.31
   7/4/14	475
   14/4/14	567.54
   21/4/14	469
   28/4/14	502.16
   5/5/14	456
   12/5/14	510.9
   19/5/14	648.66
   26/5/14	752.71
   2/6/14	750
   9/6/14	671.71
   16/6/14	690
   23/6/14	665
   30/6/14	661.2
   7/7/14	692.14
   14/7/14	614.12
   21/7/14	600.84
   28/7/14	665.93
   4/8/14	687.76
   11/8/14	584.97
   18/8/14	543
   25/8/14	510.53
   1/9/14	537.92
   8/9/14	562.43
   15/9/14	424.44
   22/9/14	460.15
   29/9/14	353.36
   6/10/14	481.64
   13/10/14	485.55
   20/10/14	449.98
   27/10/14	419.9
   3/11/14	440.98
   10/11/14	463.96
   17/11/14	448.09
   24/11/14	471.5
   1/12/14	476
   8/12/14	419.55
   15/12/14	434.97
   22/12/14	443.46
   29/12/14	362.8
   5/1/15	350.09
   12/1/15	290.02
   19/1/15	480.51
   26/1/15	289.48
   2/2/15	309.59
   9/2/15	323.9
   16/2/15	323.5
   23/2/15	354.85
   2/3/15	351.34
   9/3/15	405.86
   16/3/15	349.82
   23/3/15	380
   30/3/15	320.56
   6/4/15	379.94
   13/4/15	365
   20/4/15	300
   27/4/15	324.68
   4/5/15	295.91
   11/5/15	345.03
   18/5/15	327.36
   25/5/15	369.69
   1/6/15	328.8
   8/6/15	320.5
   15/6/15	312.87
   22/6/15	325.62
   29/6/15	362.18
   6/7/15	443.58
   13/7/15	412.15
   20/7/15	401.96
   27/7/15	415
   3/8/15	362.04
   10/8/15	329.08
   17/8/15	357.53
   24/8/15	320.4
   31/8/15	349.46
   7/9/15	330.8
   14/9/15	323.27
   21/9/15	346.48
   28/9/15	350.66
   5/10/15	339.59
   12/10/15	373.53
   19/10/15	400.01
   26/10/15	477.69
   2/11/15	551.39
   9/11/15	471.79
   16/11/15	476.89
   23/11/15	518.39
   30/11/15	540.58
   7/12/15	605.46
   14/12/15	616.24
   21/12/15	581.21
   28/12/15	582.38
   4/1/16	642.2
   11/1/16	554.28
   18/1/16	573.92
   25/1/16	532.58
   1/2/16	529.39
   8/2/16	567.05
   15/2/16	609.61
   22/2/16	606.68
   29/2/16	548.07
   7/3/16	543.69
   14/3/16	584.58
   21/3/16	589.97
   28/3/16	585.82
   4/4/16	555.66
   11/4/16	574.93
   18/4/16	616.19
   25/4/16	588.28
   2/5/16	655.87
   9/5/16	642.67
   16/5/16	612.75
   23/5/16	701.27
   30/5/16	788.69
   6/6/16	903.09
   13/6/16	1053.05
   20/6/16	905.65
   27/6/16	897.08
   4/7/16	871.54
   11/7/16	895.01
   18/7/16	893.52
   25/7/16	823.18
   1/8/16	787.93
   8/8/16	750.5
   15/8/16	760
   22/8/16	770
   29/8/16	815.6
   5/9/16	814
   12/9/16	834.99
   19/9/16	786.2
   26/9/16	819.42
   3/10/16	815.57
   10/10/16	854
   17/10/16	861.02
   24/10/16	925
   31/10/16	925.83
   7/11/16	931.9
   14/11/16	1000.52
   21/11/16	1002.97
   28/11/16	1024.27
   5/12/16	1075.2
   12/12/16	1106.2
   19/12/16	1235.94
   26/12/16	1381.4
   2/1/17	1244.41
   9/1/17	1095.16
   16/1/17	1223.2
   23/1/17	1238.34
   30/1/17	1347.74
   6/2/17	1341.48
   13/2/17	1375.95
   20/2/17	1553.46
   27/2/17	1690.27
   6/3/17	1649.1
   13/3/17	1362.27
   20/3/17	1277.61
   27/3/17	1472.88
   3/4/17	1612.83
   10/4/17	1588.75
   17/4/17	1683.46
   24/4/17	1781.71
   1/5/17	2196.67
   8/5/17	2595.07
   15/5/17	2860.85
   22/5/17	3094.79
   29/5/17	3493.27
   5/6/17	3889.46
   12/6/17	3588.86
   19/6/17	3503.31
   26/6/17	3342.76
   3/7/17	3415.51
   10/7/17	2510
   17/7/17	3541.5
   24/7/17	3529.74
   31/7/17	4060.53
   7/8/17	5318.14
   14/8/17	5298.76
   21/8/17	5620
   28/8/17	6018.4
   4/9/17	5319.46
   11/9/17	4593.05
   18/9/17	4625.38
   25/9/17	5565.36
   2/10/17	5887.35
   9/10/17	7226.76
   16/10/17	7713.93
   23/10/17	8018.65
   30/10/17	9692.39
   6/11/17	7924.89
   13/11/17	10693.55
   20/11/17	12297.99
   27/11/17	15024.19
   4/12/17	21184.87
   11/12/17	25986.55
   18/12/17	18939.79
   25/12/17	19050.74
   1/1/18	22862.21
   8/1/18	19041.51
   15/1/18	15148.37
   22/1/18	14445.12
   29/1/18	10225.82
   5/2/18	10382.72
   12/2/18	13338.45
   19/2/18	12300.72
   26/2/18	14763.94
   5/3/18	12143.73
   12/3/18	10646.88
   19/3/18	11039.19
   26/3/18	8835.98
   2/4/18	9130.39
   9/4/18	10654.32
   16/4/18	11357.21
   23/4/18	12432.76
   30/4/18	12682.62
   7/5/18	11560.03
   14/5/18	11318.46
   21/5/18	9752.02
   28/5/18	10233.1
   4/6/18	8956.31
   11/6/18	8717.19
   18/6/18	8252.91
   25/6/18	8489.05
   2/7/18	8953.63
   9/7/18	8555.52
   16/7/18	9947.28
   23/7/18	11114.06
   30/7/18	9559.81
   6/8/18	8719.77
   13/8/18	8920.44
   20/8/18	9172.49
   27/8/18	10081.22
   3/9/18	8802.43
   10/9/18	9058.83
   17/9/18	9118.22
   24/9/18	9139.68
   1/10/18	9264.69
   8/10/18	8735.74
   15/10/18	9005.48
   22/10/18	9019.61
   29/10/18	8908.97
   5/11/18	8841.39
   12/11/18	7579.24
   19/11/18	5435.57
   26/11/18	5586.65
   3/12/18	4914.89
   10/12/18	4440.44
   17/12/18	5596.18
   24/12/18	5456.26
   31/12/18	5686.6
   7/1/19	4908.14
   14/1/19	4962.34
   21/1/19	4942.09
   28/1/19	4734.24
   4/2/19	5132.33
   11/2/19	5083.2
   18/2/19	5213.99
   25/2/19	5340.09
   4/3/19	5555.14
   11/3/19	5626.45
   18/3/19	5617.53
   25/3/19	5738.09
   1/4/19	7253.71
   8/4/19	7214.66
   15/4/19	7437.26
   22/4/19	7405.25
   29/4/19	8120.41
   6/5/19	9962.31
   13/5/19	11884.94
   20/5/19	12617.35
   27/5/19	12606.94
   3/6/19	10983.83
   10/6/19	12961.26
   17/6/19	15572.87
   24/6/19	15180.16
   1/7/19	16368.05
   8/7/19	14657.08
   15/7/19	15057.73
   22/7/19	13891.59
   29/7/19	16132.89
   5/8/19	17037.56
   12/8/19	15348.79

A randomized controlled experiment has 50 participants, of whom 20 are women. A simple random sample of 25 participants are assigned to the treatment group and the remainder to the control group.

a) Say whether the following statement is true or false. If it is true, provide a math expression for the chance. If it is false, provide math expressions for the two chances.

?(the treatment group has 16 women) = ?(the control group has 16 women)P(the treatment group has 16 women) = P(the control group has 16 women)

b) Say whether the following statement is true or false, and justify your answer.

The event "the treatment group has 16 women" is independent of the event "the control group has 16 women".

c) Write a math expression for the chance that there are at least six women in both groups.

[Hint: This can be done by just thinking about the women in one of the groups. Any other way will prove quite a bit harder.]

The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution. 1285 1250 1187 1236 1268 1316 1275 1317 1275

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

x = ____A.D.

s = _____yr

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

lower limit A.D.

upper limit A.D.

________________________________________________________________________

How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean price x and sample standard deviation s. (Round your answers to two decimal places.)

(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price μ of all summer sleeping bags. (Round your answers to two decimal places.)

The accompanying data set provides the closing prices for four stocks and the stock exchange over 12 days:

With the help of the Excel Exponential Smoothing tool, I was able to forecast each of the stock prices using simple exponential smoothing with a smoothing constant of 0.3 (ie, damping factor of 0.7). I was also able to calculate the MAD of each of the stocks:

MAD of Stock A = 1.32

MAD of Stock B = 0.37

MAD of Stock C = 0.41

MAD of Stock D = 0.26

MAD of Stock Exchange = 83.85

Help me to calculate the Mean Square Error (MSE) of the stocks.