Explain what sampling is and why do researcher use it? What are some factors that need to be considered in conducting a sample? What are some potential problems with sampling? Why do so many of life’s...

Explain what sampling is and why do researcher use it? What are some factors that need to be considered in conducting a sample? What are some potential problems with sampling?

1. 
   Why do so many of life’s events share the same characteristics with Central Limit Theorem? Why are estimations and confidence intervals important? When might systematic sampling be biased? Explain. What roles do confidence intervals and estimation play in the selection of sample size?
   


2. 
   What is a confidence interval, what is it used for, and what are some attributes ofa confidence interval? How do you see something like this being used presently or in the future at your place of deployment or in some group that you are involved in out side of your present position?
   

4.)
A man is on trial accused of murder in the first degree. The prosecutor presents evidence that he hopes will convince the jury to reject the hypothesis that the man is innocent. This situation can be modeled as a significance test with the following hypotheses:


Ho: The defendant is innocent


H1: The defendant is not innocent


Suppose that the null hypothesis is rejected and alternate hypothesis is accepted. Discuss the conclusion as a Type I error, a Type II error, or a correct decision, if in fact the defendant is innocent.

1. 
   Why would you use a small sample to draw inference about a large population? Why is a
   t-statistic, as opposed to a
   z-statistic, used to test small populations?
   


2. 
   A mayoral election race is tightly contested. In a random sample of 1,100 likely voters, 572 said that they were planning to vote for the current mayor. Based on this sample, what is your initial hunch? Would you claim with 95% confidence that the mayor will win a majority of the votes? Explain.
   


3. 
   In statistics, we will talk about a population having a family of distributions. What do we mean by this statement? How is it important in statistical analysis?
   


4. 
   What is an example of a research problemat your station that would benefit from the use of either descriptive statistics or probability distribution statistics? How would you apply what you are learning to address the problem?
   


5. 
   What are the characteristics of a normal distribution? What is the purpose of standardized scores? Compare and contrast z and t scores. Discuss theattributes and utilization of each. Discuss the area under the curve and calculations involving this information.
   


6. 
   What is probability? Why is probability such an important concept in statistics? How does probability fit into the decision making process?
   

1.
What are the input and the output of linear regression?

1. What does the coefficient of determination measure?

1. What is the purpose of measuring correlation?

1. Answer the following questions using this data.

A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected:


What is the dependent variable?
What is the independent variable?
What is the
Y-intercept of the linear equation?
What is the slope of the linear equation?
What is the value of the coefficient of correlation?

1. The relationship between interest rates as a percent (X) and housing starts (Y) is given by the linear equation = 4094 – 269X. Answer these questions.

What will be the number of housing starts if the interest rate is 8.25%?
What will be the number of housing starts if the interest rate rose to 16%?
What happens to housing starts as interest rates fall?
6. If the regression equation is = 2 – 0.4X, what is the value of when
X
= –3?
7. In the least squares equation, = 10 + 20X
the value of 20 indicates
8. If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?
9. Based on the regression equation, we can
A) predict the value of the dependent variable given a value of the independent variable.
B) predict the value of the independent variable given a value of the dependent variable.
C) measure the association between two variables.
D) all of the above.
10. What is the general form of the regression equation?
A) =
ab


B) =
a
+
bX


C) =
a
–
bX


D) =
abX


11. The strength of the correlation between two variables depends on the sign of the coefficient of correlation.
True or False
12. The correlation coefficient is the proportion of total variation in
Y
that is explained by
X.
True or False
13. What does a coefficient of correlation of 0.70 infer?
A) Almost no correlation because 0.70 is close to 1.0
B) 70% of the variation in one variable is explained by the other
C) Coefficient of determination is 0.49
D) Coefficient of non-determination is 0.30
14. If we are studying the relationship between high school performance and college performance, and want to predict college performance, what kind of variable is high school performance? ________________
15. The regression coefficient,
a, is the point where the regression line __________ the
Y-axis.

Homework 4 (worth 4 points)
1. The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.

Answer these questions.

Assuming a normal distribution, approximately how many scored 90 or higher?
A) 0.4979
B) 0.0021
C) 0.9979
D) 2.86
Assuming a normal distribution, approximately how many scored greater than 65?
A) 0.2611
B) 0.2389
C) 0.7611
D) –0.714
2. Two business major students, in two different sections of economics, were comparing test scores. The following gives the students scores, class mean, and standard deviation for each section.



Answer these questions.

Which student scored better compared to the rest of the section?
What is the z-score of the student from section 1?
What is the z-score of the student from section 2?
3. The weight of a bag of corn chips is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces.

Answer these questions.

What is the probability that a bag of corn chips is less than 20 ounces?
What is the probability that a bag of corn chips weighs more than 21 ounces?
What is the probability that a bag of corn chips weighs between 20.75 and 23.25 ounces?
4. A sample of 500 evening students revealed that their annual incomes from employment in industry during the day were normally distributed with a mean income of $30,000 and a standard deviation of $3,000.

Answer these questions.

How many students earned more than $30,000?
How many students earned between $27,000 and $33,000?
How many students earned less than $22,500?
5. What proportion of the area under a normal curve is to the right of z = –1.21?
6. What type of probability distribution is the normal distribution?
7. In a standard normal distribution, = ______ and = ______.
8. About what percent of the area under the normal curve is within plus two and minus two standard deviation of the mean?
9. Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 percent of production based on past experience. Past records indicate that, on the average, 4,000 units of a small assembly are produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. If the bonus is paid on the upper 5 percent of production, the bonus will be paid on how many units or more?
A) 6255
B) 5120
C) 3196
D) 4099
10. A random sample of 85 group leaders, supervisors, and similar personnel revealed that a person spent an average 6.5 years on the job before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval for the population mean?
A) 6.99 and 7.99
B) 4.15 and 7.15
C) 6.14 and 6.86
D) 6.49 and 7.49
11. Which statement(s) is/are correct about the t distribution?
A) Mean = 0
B) Symmetric
C) Based on degrees of freedom
D) All of the above are correct
E) None of the above is correct
12. A sample of 20 is selected from the population. To determine the appropriate critical t-value what number of degrees of freedom should be used?
A) 20
B) 19
C) 21
D) 25
13. A confidence interval for a population mean
A) estimates the population range
B) estimates a likely interval for a population mean
C) estimates a likelihood or probability
D) estimates the population standard deviation
14. The distribution of Student's t has
A) a mean of zero and a standard deviation of one
B) a mean of one and a standard deviation of one
C) a mean of zero and a standard deviation that depends on the sample size
D) a mean that depends on the sample size and a standard deviation of one
15. The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons. The sample standard deviation is 5.0 tons. What is the 95 percent interval for the population mean?
A) 10.80 and 20.80
B) 14.40 and 17.20
C) 14.36 and 17.24
D) 14.00 and 17.00
16. In order to construct the 99 percent confidence interval, how many standard errors of the mean from the hypothesized population mean must you go? __________
17. When we use a confidence interval to reach a conclusion about the population mean, we are applying a type of reasoning or logic called
A) descriptive statistics
B) the normal distribution
C) statistical inference
D) graphics
Use the following to answer questions 18 and 19:
A student wanted to quickly construct a 95% confidence interval for the average age of students in her statistics class. She randomly selected 9 students. Their average age was 19.1 years with a standard deviation of 1.5 years.
18. What is the best point estimate for the population mean?
A) 2.1 years
B) 1.5 years
C) 19.1 years
D) 9 years

19. What is the 95% confidence interval for the population mean?
A) [0.97, 3.27]
B) [15.64, 22.56]
C) [17.97, 20.23]
D) [17.95, 20.25]
20. A pharmaceutical company wanted to estimate the population mean of monthly sales for their 250 sales people. Forty sales people were randomly selected. Their mean monthly sales were $10,000 with a standard deviation of $1000. Construct a 95% confidence interval for the population mean.
A) [9,690.1, 10,309.9]
B) [9,715.5, 10,284.5]
C) [8,040, 11,960]
D) [8,000, 12,000]
21. A company wants to estimate next years total revenue. Why is an interval estimate preferred to a point estimate? (2 points)