Over the past 6​ years, Elk County Telephone has paid the dividends shown in the following​ table. he​ firm's dividend per share in

2020 is expected to be $1.27

2019 $1.22

2018 $1.17

2017 $1.12

2016 $1.08

2015 $1.04

2014 $1.00

a.  If you can earn 11​% on​ similar-risk investments, what is the most you would be willing to pay per share in 2019​, just after the $1.22 dividend?

b.  If you can earn only 8% on​ similar-risk investments, what is the most you would be willing to pay per​ share?

c.  Compare your findings in parts a and ​b, what is the impact of changing risk on share​ value?

10.12 A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers and stored in Bank1. These data are:

Suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 p.m. lunch period. Data are collected from a random sample of 15 customers and stored in Bank2. These data are:

• a. Assuming that the population variances from both banks are equal, is there evidence of a difference in the mean waiting time between the two branches? (Use α=0.05.α=0.05. alpha equals , 0.05.)

• b. Determine the p-value in (a) and interpret its meaning.

• c. In addition to equal variances, what other assumption is necessary in (a)?

• d. Construct and interpret a 95% confidence interval estimate of the difference between the population means in the two branches.

A population of values has a normal distribution with μ = 194 μ = 194 and σ = 13.4 σ = 13.4 . You intend to draw a random sample of size n = 127 n = 127 . Find the probability that a single randomly selected value is greater than 197.3. P(X > 197.3) = Find the probability that a sample of size n = 127 n = 127 is randomly selected with a mean greater than 197.3. P(M > 197.3) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

For each of the following examples of tests of hypothesis about µ, show the rejection and nonrejection regions on the t-distribution curve. (a) A two-tailed test with α = 0.01 and n = 15 (b) A left-tailed test with α = 0.005 and n = 25 (c) A right-tailed test with α = 0.025 and n = 22

Demonstrate the relationship between two variables. You will be required to use the least squares approach as well as use software (SPSS preferred) to perform analyses that will yield the coefficient of correlation, the coefficient of determination, and a simple linear regression analysis

The average height of professional basketball players is around 6 feet 7 inches, and the standard deviation is 3.89 inches. Assuming Normal distribution of heights within this group

(a) What percent of professional basketball players are taller than 7 feet?

(b) If your favorite player is within the tallest 20% of all players, what can his height be?

(1 point) A random sample of 100100 observations from a population with standard deviation 19.788150778587319.7881507785873 yielded a sample mean of 93.893.8.
(a)    Given that the null hypothesis is ?=90μ=90 and the alternative hypothesis is ?>90μ>90 using ?=.05α=.05, find the following:

(i)    critical z/t score    

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Equation Editor

(ii)    test statistic ==

(b)    Given that the null hypothesis is ?=90μ=90 and the alternative hypothesis is ?≠90μ≠90 using ?=.05α=.05, find the following:

(i)    the positive critical z/t score    

(ii)    the negative critical z/t score    

(iii)    test statistic ==

The conclusion from part (a) is:

A. There is insufficient evidence to reject the null hypothesis
B. Reject the null hypothesis
C. None of the above

The conclusion from part (b) is:

A. Reject the null hypothesis
B. There is insufficient evidence to reject the null hypothesis
C. None of the above

0.2 point for writing the hypothesis in symbolic form.

0.2 point for determining the value of the test statistic.

0.2 point for finding the critical value OR the p-value.

0.2 point for determining if you should reject the null hypothesis or fail to reject the null hypothesis.

0.2 point for writing a conclusion addressing the original claim.

All work must be shown

A study is done to test the claim that Company A retains its workers longer than Company B. Company A samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company B samples 21 workers, and their average time with the company is 4.6 years with a standard deviation of 0.9. The populations are normally distributed.

Historically, 20% of graduates of the engineering school at a major university have been women. In a recent, randomly selected graduating class of 210 students, 58 were females. Does the sample data present convincing evidence that the proportion of female graduates from the engineering school has shifted (changed)? Use α = 0.05. Determine what type of error (Type I or II) could be made in the question above.

1. The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained.

Analysis of Variance SOURCE DF Regression 1 Error 7 Total 8

Predictor Coef Constant 20.000 X

Adj SS 41587.3

51984.1

SE Coef T-value 3.2213 6.21 1.3626 5.29

(a) How many apartment buildings are in the sample?
(b) What is the value of b1.
(c) Write the estimated regression equation.
(d) Use the F statistic to test the significance of the relationship at a 0.05 level of

significance.
(e) Predict the selling price of an apartment with gross rents of $50 000.

Question 2

Raw data: 19 14 25 17 29 24 36 23 9 26 22 31 19 28 8

2.1 Group the data into a frequency distribution with a lowest class lower limit of 8 and class width of 7, then draw an ogive curve and use it to estimate the mean

General guidelines:

Use EXCEL or PHStat to do the necessary computer work.

Do all the necessary analysis and hypothesis test constructions, and explain completely.

Read the textbook Chapter 13. Imagine that you are managing a mobile phone company. You want to construct a simple linear regression model to capture and represent the relationship between the number of customers and the annual sales level for a year with 95% confidence. You had conducted a pilot study for the past fifteen years and collected yearly observations as given in the following data.Where the number of customers in a year is represented by the Profiled Customers variable, measured by million customers unit, and the sales level is represented by the Annual Sales variable, measured by million US-dollars unit.

1) Investigate the agreement between the model and the data set for:

A) LINEARITY.

A1) Construct the "Dot Plot", a.k.a. "Scatter Plot," for this data. Visually inspect for the linear relationship between the number of customers and the sales level. Make comments based on your observations.

A2) Conduct the F-Test for linearity.

A3) If you have seen evidence of linearity in the F-Test, then:

Conduct the t-Test for the partial slope.

Construct the 95% Confidence Interval Estimator for the partial slope.

Thus, make comments about the linear relationship between the Profiled Customers and the Annual Sales, based on the partial slope information.

B) NORMALITY.

Construct the "Normal Probability Plot" for the Annual Sales variable, and make comments about the normality of annual sales level, based on your observations.

C) HOMOSCEDASTICITY.

Construct the "Residual Plot" and make comments about the variance of annual sales level, based on your observations.

D) INDEPENDENCE.

This data set is a Time-Series. Hence, investigate for the independence of observations in this time-series, based on the Durbin-Watson test.

2) If there is evidence of agreement between the model and data, and independence of observations, then construct the simple linear regression equation for this data set, based on the least square error method.

2A) Construct the 95% confidence interval for the actual average annual sales level for all the years that you have 5 million customer in a year,

2B) Construct the 95% prediction interval for the actual annual sales level for one year that you have 5 million customers in that year.

An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?

Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=0.1 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H 0 . Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test.

The population average cholesterol content of a certain brand of egg is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.

i) Find the third quartile for the average cholesterol content for 25 eggs.

ii)If we are told the average for 25 eggs is less than 220 mg, what is the probability that the average is less than 210.