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## Case 3/4

Description

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.
Choose one design method from the list below. Using your example, make a list of 2 or 3 advantages and 2 or 3 disadvantages for using the method. (2 pts)
Simple random sampling
Systematic sampling
Stratified sampling
Cluster sampling
The name of each student in a class is written on a separate card. The cards are placed in a bag. Three names are picked from the bag. Identify which type of sampling is used and why. (2 pts)
A phone company obtains an alphabetical list of names of homeowners in a city. They select every 25th person from the list until a sample of 100 is obtained. They then call these 100 people to advertise their services. Does this sampling plan result in a random sample? What type of sample is it? Explain. (2 pts)
The manager of a company wants to investigate job satisfaction among its employees. One morning after a meeting, she talks to all 25 employees who attended. Does this sampling plan result in a random sample? What type of sample is it? Explain. (2 pts)
An education expert is researching teaching methods and wishes to interview teachers from a particular school district. She randomly selects 10 schools from the district and interviews all of the teachers at the selected schools. Does this sampling plan result in a random sample? What type of sample is it? Explain. (2 pts)
Fifty-one sophomore, 42 junior, and 55 senior students are selected from classes with 516, 428, and 551 students respectively. Identify which type of sampling is used and explain your reasoning. (2 pts)
You want to investigate the workplace attitudes concerning new policies that were put into effect. You have funding and support to contact at most 100 people. Choose a design method and discuss the following:
Describe the sample design method you will use and why. (2 pts)
Specify the population and sample group. Will you include everyone who works for the company, certain departments, full or part-time employees, etc.? (2 pts)
Discuss the bias, on the part of both the researcher and participants. (2 pts)
A local newspaper wanted to gather information about house sales in the area. It distributed 25,000 electronic surveys to its readers asking questions about house sales in the past 6 months. Of the surveys sent out, 3.2% were returned. The results found that 92% of people did not sell their house in the past 6 months and 85% of people would expect a loss if they sold their house. The writer wants to use these results to conclude that the housing market is declining, and we are headed for a recession.
Explain the bias and sampling error in this study. (2 pts)
Should the writer conclude that the housing market is declining based upon this data? (2 pts)
Why or why not? (2 pts)
A homeowner is getting carpet installed. The installer is charging her for 250 square feet. She thinks this is more than the actual space being carpeted. She asks a second installer to measure the space to confirm her doubt. Write the null hypothesis Ho and the alternative hypothesis Ha. (2 pts)
Drug A is the usual treatment for depression in graduate students. Pfizer has a new drug, Drug B, that it thinks may be more effective. You have been hired to design the test program. As part of your project briefing, you decide to explain the logic of statistical testing to the people who are going to be working for you.
Write the research hypothesis and the null hypothesis. (2 pts)
Then construct a table like the one below, displaying the outcomes that would constitute Type I and Type II error. (2 pts)
Write a paragraph explaining which error would be more severe, and why. (2 pts)

Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variation from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces):

5.95
6.10
5.98
6.01
6.25
5.85
5.91
6.05
5.88
5.91
Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle?
State the hypothesis you will test. (2 pts)
Calculate the test statistic. (2 pts)
Find the P-value. (2 pts)
What is the conclusion? (2 pts)
Calculate a Z score when X = 20, μ = 17, and σ = 3.4. (2 pts)
Using a standard normal probabilities table, interpret the results for the Z score in Problem 12. (2 pts)
Your babysitter claims that she is underpaid given the current market. Her hourly wage is \$12 per hour. You do some research and discover that the average wage in your area is \$14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability. Based on your findings, should you give her a raise? Explain your reasoning as to why or why not. (2 pts)
Tutor O-Rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math portion of the SAT is μ=350 and σ=35. The 100 students who completed the tutoring program had an average score of 385 points.
Is the students’ average score of 385 points significant at the 5% and 1% levels to support Tutor O-Rama’s claim of at least a 50-point increase in the SAT score? (2 pts)
Is the Tutor O-Rama students’ average score of 385 points significantly different at the 5% and 1% levels from the average score of 350 points on the math portion of the SAT? What conclusion can you make, based on your results, about the effectiveness of Tutor O-Rama’s tutoring? (2 pts)

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.
The final exam scores listed below are from one section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?
99 34 86 57 73 85 91 93 46 96 88 79 68 85 89
The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
If you know the standard deviation, how do you find the variance?
To get the best deal on a stereo system, Louis called 8 out of 20 appliance stores in his neighborhood and asked for the cost of a specific model. Below is the sample data set of prices he collected:
\$216 \$135 \$281 \$189 \$218 \$193 \$299 \$235
Find the standard deviation.
The Company collected a sample of the salaries of its employees. There are 70 salary data points summarized in the frequency distribution below:
Salary
Number of Employees
5,001–10,000
8
10,001–15,000
12
15,001–20,000
20
20,001–25,000
17
25,001–30,000
13
Find the standard deviation.
Find the variance.
6. Calculate the mean and variance of the sample data set provided below. Show and explain your steps. Round to the nearest tenth.
14, 16, 7, 9, 11, 13, 8, 10
Create a frequency distribution table for the number of times a number was rolled on a die. (It may be helpful to print or write out all of the numbers so none are excluded.)
3, 5, 1, 6, 1, 2, 2, 6, 3, 4, 5, 1, 1, 3, 4, 2, 1, 6, 5, 3, 4, 2, 1, 3, 2, 4, 6, 5, 3, 1
Answer the following questions using the frequency distribution table you created in No. 7.
Which number(s) had the highest frequency?
How many times did a number of 4 or greater get thrown?
How many times was an odd number thrown?
How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?
The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the sample data below, find the following for each sample:
Range
Standard deviation
Variance
Lastly, compare the two sets of results.
Company
Wait times in seconds
Big Burger Company
105
67
78
120
175
115
120
59
The Cheesy Burger
133
124
200
79
101
147
118
125
What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?