**Subject Mathematics General Statistics**

## Question

• Simple random sampling

• Systematic sampling

• Stratified sampling

• Cluster sampling

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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:

a. Describe the sample design method you will use and why.

b. Specify the population and sample group. Will you include everyone who works for the company, certain departments, full or part-time employees, etc.?

c. Discuss the bias, on the part of both the researcher and participants.

8. 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.

a. Should the writer conclude that the housing market is declining based upon this data?

b. Why or why not?

9. 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.

10. 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.

a. Then construct a table like the one below, displaying the outcomes that would constitute Type I and Type II error.

b. Write a paragraph explaining which error would be more severe, and why.

11. 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.

a. Calculate the test statistic.

b. Find the P-value.

c. What is the conclusion?

12. Calculate a Z score when X = 20, μ = 17, and σ = 3.4.

13. Using a standard normal probabilities table, interpret the results for the Z score in Problem 12.

14. 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.

15. 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?

a. 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?

## Solution Preview

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Advantages of stratified sampling:

1. The main advantage is that here the cost per observation is generally very less .

2. For each subgroup estimates of the parameters can be generated , and the accuracy is better than simple random sampling.

Disadvantages:

1. It is not easy to implement.

2. It is more complex as compare to random sampling.

2. Ans: Since we are choosing 3 name from the bag which is mixed in the name of students of this class. Therefor it is an example of random sampling

3. Ans: Since we are selecting the name of 25th person until sample...

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