In 1997, the average household expenditure for energy was $1,338, according to data obtained from the U.S. Department of Energy.  An economist claims that energy usage today is different from its 1997 level.  In a random sample of 36 households, the economist found the mean expenditure, adjusted for inflation, for energy in 2004 to be $1,423. with a sample standard deviation s = 360.

At a 95% level of confidence (α = .05), we wish to test the economists claim.

1. State the Null Hypothesis and Alternate Hypothesis for this experiment.

2.What is the p-value and decision of this research?

3.State the conclusion.

4.State the Type I error for this Hypothesis Test and the corresponding probability of a Type I error occurring in this experiment.

5.In order to decrease the probability of a Type I error, we would do the following before conducting this experiment:

Below are means, standard deviations, and sample sizes of three different data sets. Estimate the 90% confidence interval for dataset A, 95% for data set B, and 99% for set C.

Set A: mean=6300, standard deviation= 300, n=200

Set B: mean=65, standard deviation= 15, n=75

Set C: mean=93, standard deviation= 37, n=200

Kroger runs Buy One Get One (BOGO) promotions every year to promote charcoal for Memorial Day. Their data indicates that 76 customers per day per store purchase this deal every spring and the standard deviation historically is 12 customers. Assume that the population is normally distributed. What is the probability that for a random sample of 15 days, at least 70 customers per day will buy charcoal with the BOGO?

1) 0.6915

2) 0.9772

3) 0.0262

4)0.9738

The IQs of students at Wilson Elementary School were measured recently and found to be normally distributed with a mean of 110 and a standard deviation of 13. What is the probability that a student selected at random will have the following IQs? (Round your answers to four decimal places.)

(a) 140 or higher

(b) 115 or higher

(c) between 110 and 115

(d) 100 or less

Suppose the installation time in hours for a software on a laptop has probability density function f(x) = (4/3) (1 − x³ ), 0 ≤ x ≤ 1.

(a) Find the probability that the software takes between 0.3 and 0.5 hours to be installed on your laptop.

(b) Let X₁, . . . , X₃₀ be the installation times of the software on 30 different laptops. Assume the installation times are independent. Find the probability that the average installation time is between 0.3 and 0.5 hours. Cite the theorem you use.

(c) Instead of taking a sample of 30 laptops as in the previous question, you take a sample of 60 laptops. Find the probability that the average installation time is between 0.3 and 0.5 hours. Cite the theorem you use.

 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    

equation editor

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.