Consider a stock with a beginning of the year price of 21. The stock's dividends and quarterly stock price are as follows:

The effective annual yield on this stock is ____________.

Given the following marginal utility schedule for good X and good Y for an individual A, given that the price of X and the price of Y are both $10, and that the individual spends all his income of $70 on X and Y,

Q x          1         2       3      4      5      6        7
MUX      15       11       9      6      4      3        1
Q y           6        5       4      3      2      1        0
MUY       12        9       8      6      5      2        1

1. Provide the slope of the budget line
2. Estimate the MRS at the optimum

3. Indicate how much of X and Y the individual should purchase to maximize utility.
Select one:
a. 1. Provide the slope of the budget line: -10
2. Estimate the MRS at the optimum: -10

3. Indicate how much of X and Y the individual should purchase to maximize utility. 4X and 3Y
b. 1. Provide the slope of the budget line: -1
2. Estimate the MRS at the optimum:-1

3. Indicate how much of X and Y the individual should purchase to maximize utility: 6X and 6Y
c. 1. Provide the slope of the budget line: -10/70
2. Estimate the MRS at the optimum: -10/70

3. Indicate how much of X and Y the individual should purchase to maximize utility. 1X and 6Y
d. 1. Provide the slope of the budget line: -1
2. Estimate the MRS at the optimum: -1

3. Indicate how much of X and Y the individual should purchase to maximize utility. 7X and 0Y
e. 1. Provide the slope of the budget line: -1
2. Estimate the MRS at the optimum: -1

3. Indicate how much of X and Y the individual should purchase to maximize utility: 4X and 3Y

Solve the following initial value problems

y'' + y = 2/cos x , y(0) = y'(0) = 2

x^3 y''' − 6xy' + 12y = 20x^4, x > 0, y(1) = 8/3 , y'(1) = 50/3 , y''(1) = 14

x^2 y'' − 2xy' + 2y = x^2, x > 0, y(1) = 3, y'(1) = 5

. Desert iguanas are thought to use their tongues to obtain information about their environment by sampling odours that may be important for their survival and reproductive success. Pedersen (1988) studied the rates of tongue extrusions in desert iguanas who were exposed to sands collected from a = 5 different environments. These environments consisted of a1 = clean sand, a2 = sand from an iguana’s home cage, a3 = sand from cages housing other iguanas, a4 = sand from cages housing western whiptail lizards, and a5 = sand from cages housing desert kangaroo rats. (The latter two species are frequently seen in close contact with desert iguanas in their natural habitat). A total of n = 10 iguanas served in the experiment. Each was tested in each condition on successive days; the order of testing was randomly determined for each animal. The iguanas were videotaped during each 10-minute test session; the response measure was the number of tongue extrusions observed during each test session.

Subject        a1        a2        a3        a4        a5

1              8         5         14        10        16

2              2         2         0         2         4

3              1         0         2         1         3

4              4         3         3         5         6

5              0         0         0         0         0

6              2         5         3         5         12

7              2         1         1         2         5

8              0         0         0         3         11

9              0         1         0         0         3

10             3         2         1         2         8

8. Desert iguanas are thought to use their tongues to obtain information about their environment by sampling odours that may be important for their survival and reproductive success. Pedersen (1988) studied the rates of tongue extrusions in desert iguanas who were exposed to sands collected from a = 5 different environments. These environments consisted of a1 = clean sand, a2 = sand from an iguana’s home cage, a3 = sand from cages housing other iguanas, a4 = sand from cages housing western whiptail lizards, and a5 = sand from cages housing desert kangaroo rats. (The latter two species are frequently seen in close contact with desert iguanas in their natural habitat). A total of n = 10 iguanas served in the experiment. Each was tested in each condition on successive days; the order of testing was randomly determined for each animal. The iguanas were videotaped during each 10-minute test session; the response measure was the number of tongue extrusions observed during each test session.

1. Calculate the average return over the last 3 years.

2. Calculate the standard deviation of your company’s returns over the last 3 years.

[I will make sure to give thumbs up to those who answer]

Between being a housewife and caring for her family and aging parents, Ashley is a very busy lady. Below are the number of errands (trips to the grocery store, school events, pharmacy, doctor's office, etc.) which Ashley has run on each day in June.

a. Calculate the mean for the above set of errands.

Round your answer to two decimal places.

Mean = ?????errands

b. Calculate the median for the above set of errands.

Round your answer to one decimal place.

Median = ????? errands

c.  What is the mode for the above set of errands?

Enter your answer as a whole number.

Mode = ???? errands

1. Two samples are taken with the following numbers of successes and sample sizes
r1r1 = 32 r2r2 = 30
n1n1 = 68 n2n2 = 92

Find a 88% confidence interval, round answers to the nearest thousandth.
< p1−p2 <

Box 1: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 2: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

2.

Two samples are taken with the following sample means, sizes, and standard deviations
¯x1x¯1 = 33 ¯x2x¯2 = 24
n1n1 = 57 n2n2 = 73
s1s1 = 3 s2s2 = 4

Estimate the difference in population means using a 90% confidence level. Use a calculator, and do NOT pool the sample variances. Round answers to the nearest hundredth.
< μ1-μ2 <

Box 1: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 2: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Please explain how to get the answer using a calculator thank you. There is 2 questions because is the third time I have had to post this question because the answer was wrong.

Hypothesis Testing and Confidence Intervals

The Reliable Housewares store manager wants to learn more about the purchasing behavior of its

"credit" customers. In fact, he is speculating about four specific cases shown below (a) through (d) and

wants you to help him test their accuracy.

b. The true population proportion of credit customers who live in an urban area exceeds 55%

i. Using the dataset provided in Files perform the hypothesis test for each of the above speculations (a) through (d) in order to see if there is an statistical evidence to support the manager’s belief. In each case,

oUse the

Seven Elements of a Test of Hypothesis, in Section 7.1 of your textbook (on or about Page 361) or the Six Steps of Hypothesis Testing I have identified in the addendum.

oUse α=2%for all your analyses,

oExplain your conclusion in simple terms,

oIndicate which hypothesis is the“claim”,

o Compute the p-value,

o Interpret your results,

ii.Follow your work in (i) with computing a 98% confidence interval for each of the variables

described in (a) though (d). Interpret these intervals.

iii.

Write an executive summary for the Reliable Housewares store manager about your analysis,

distilling down the results in a way that would be understandable to someone who does not

know statistics. Clear explanations and interpretations are critical.

In the binomial function, negative binomial function, poisson distribution, I dont know what to do when we need to find a variable X. For example, If X is exactly at 0, 1 , 2, etc. Then I know that we only need to apply the formula and calculate it. However, in some cases like X <= 2, X >= 5, X > 4, etc, then I do not know how to calculate that X and how to apply the formula. Ex: If P( X >= 4) = 1 - P(X <= 3) and for X <= 3, we will calculate the sum of X = 0, X = 1, X = 2, X = 3. How to define when to use 1 - P(X <= 3) or how P(X = 4) = P(X <= 4) - P(X <= 3). It really hard for me to understand this concept. Is there any formula or any way to define it so you know when to subtract, or when to add it together? Thank you.