• Hypothesis testing is a set of core analysis tools used to answer questions about the characteristics of a population. The process involves a number of steps, varying from five to ten depending upon the author of the text being used. What are these steps and why is it so important to follow and explicitly state each step in the process? In your responses discuss the properties of hypotheses, the importance and meaning of the level of significance and the various kinds of tests we might choose from and why.
• One and Two sample hypothesis tests (see week five for the two sample tests) are either comparing a sample to a standard value or comparing to samples to each other. Thanks to the CLT and the empirical rule we can usually trust the results. But there are exceptions. These are called Type I and Type II errors.

4. The following data set represent the percentage of gold from two different

locations:

Location A

Location B

5.0 6.1 2.3 2.1 7.8 9.2 4.1 2.5 4.2 9.9 1.0 1.2

b) Now consider the two locations as a single data set. What are the mean and the standard deviation of the gold percentage for this data set?

c) Using the empirical rule, determine what range of values captures the middle 68% of the data for the combined data set. Give the lower and upper limit of this range.

d) What is the actual percentage of data points that falls between these two values? Why is it different from your answer of part c?

In a certain article, laser therapy was discussed as a useful alternative to drugs in pain management of chronically ill patients. To measure pain threshold, a machine was used that delivered low-voltage direct current to different parts of the body (wrist, neck, and back). The machine measured current in milliamperes (mA). The pretreatment experimental group in the study had an average threshold of pain (pain was first detectable) at μ = 3.02 mA with standard deviation σ = 1.29 mA. Assume that the distribution of threshold pain, measured in milliamperes, is symmetrical and more or less mound-shaped. (Round your answers to two decimal places.)

(a) Use the empirical rule to estimate a range of milliamperes centered about the mean in which about 68% of the experimental group will have a threshold of pain from                       mA to                         mA

1.) In a recent​ survey,66​% of the community favored building a police substation in their neighborhood. If 14 citizens are​ chosen, find the probability that exactly 5 of them favor the building of the police substation. Round the answer to the nearest thousandth.

a.) .357

b.) .660

c.) .015

d.) .216

2.) A coin is tossed. Find the probability that the result is heads.

a.) .5

b.) .1

c.) 1

d.) .9

3.) The mean SAT verbal score is 464 with a standard deviation of 90. Use the empirical rule to determine what percent of the scores lie between 284 and 554. Assume the data set has a bell-shaped distribution.

a.) 68%

b.) 83.9%

c.) 34%

d.) 81.5%

Please answer all three questions! Thank you!

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1249 with a standard deviation of 32 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following.

(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found between and A.D.

(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found between and A.D.

(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found between and A.D.

With work shown.

7. Calculate the number of sodium atoms in 4.66 moles of sodium.

8. What is the molar mass fo a substance if 0.6502 moles of the substance has a mass of 19.27 grams?

9. How many grams are present in 7.5 moles of Cu (NO3)2?

10. How many atoms are present in a Mg sample with a mass of 14.6 grams?

11. How many atoms of H are present in 37.6 g of NH3?

12. How many atoms are present in 0.45 moles of P4O10?

13. The empirical formula of a compound is CH2O and it's formula weight is 120.12 amu. What is the molecular formula?

14. Analysis of an unknown sample indicated the sample contained 0.140g of N and 0.320 g of O. The molar mass of the compound was determined to be 92.02 amu. What is the molecular formula of the compound?

1. Solve the problem using the employment information in the table on Alpha Corporation

1. The mean of a set of data is 5.07 and its standard deviation is 3.39. Find the z-score for a value of 9.65. _______________________
2. Which is better and corresponds to the higher relative position, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? ____________________________________
3. On a given registration day, 45 CJ majors and 25 CIS majors arrive. What is the empirical probability that the next student to arrive will be a CJ major? ______________________________

No Hand Writing please, Type your answer.

Suppose that you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next twenty-five times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 20 miles per gallon and a standard deviation of 1. Find the possible sample means you are likely to get based on your sample of twenty-five observations. Consider the intervals into which 68%, 95%, and almost all of the potential sample means will fall, using the Empirical Rule. (Round all answers to the nearest thousandth.)

About 68% of possible sample means will be in the range between ___ and ____ .

About 95% of possible sample means will be in the range between ____ and ____ .

About 99.7% of possible sample means will be in the range between ____ and ____.

Suppose that the national average for the math portion of the College Board's SAT is 513. The College Board periodically rescales the test scores such that the standard deviation is approximately 75. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.

(a) What percentage of students have an SAT math score greater than 588?

___ %

(b) What percentage of students have an SAT math score greater than 663?

___ %

(c) What percentage of students have an SAT math score between 438 and 513?

___ %

(d) What is the z-score for a student with an SAT math score of 620?

____

(e) What is the z-score for a student with an SAT math score of 405?

____

Suppose that the national average for the math portion of the College Board's SAT is 518. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.