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Simple Random Sample

Simple Random Sample. A set of measurement from a population that is a subset of the population selected in a manner such that. Every sample of size n from the population has an equal chance of being selected.

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Simple Random Sample

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  1. Simple Random Sample A set of measurement from a population that is a subset of the population selected in a manner such that • Every sample of size n from the population has an equal chance of being selected. b. Every member of the population has an equal chance of being included in the sample.

  2. Example: An all-star team is to be chosen as follows: Each of the 9 teams in the league will randomly select 2 of their 15 players. These 18 players will then form the all-star team. Is this a simple random sample? No – each possible team of 18 players does not have the same chance of being selected.

  3. Sampling Techniques Stratified The sample is divided into strata and then a random sample is taken from each strata. Example: Separate a sample of businesses according to type: medical, shipping, retail, manufacturing, financial, construction, and restaurant. Then select a random sample of 10 from each type.

  4. Systematic: We select a random starting point and then select every kth element for our sample. Example: Number all of the business. Select a starting point at random, and then use every 10th business listed until you have the desired sample size.

  5. Divide the demographic area into sections then randomly select N sections. Cluster Example: Use the zip codes to divide the state into regions. Pick a random sample of 10 Zip code areas and then include all the businesses in each selected zip code area.

  6. Experiment vs Observation Experiment: A treatment is deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured. Response Variable – the one being measured Explanatory Variable – the treatment

  7. Example: An Australian study included 588 men and women who already had some pre-cancerous skin lesions. Half got a skin cream containing a sunscreen with a sun protection factor of 17; half got an inactive cream. After 7 months, those using the sunscreen with the sun protection had fewer new pre-cancerous skin lesions. Response : # of pre-cancerous skin lesions Explanatory: Type of sunscreen Placebo: The inactive cream (acts like a control group)

  8. Other Terms Double blind experiment: Neither the individuals in the study nor the observers know which subjects are receiving the treatment. It helps to control for subtle biases. Control Group: Gets no treatment. Used to account for the influence of other variables.

  9. Observation: Based on observations – no treatments are given. Example: An ecology class used binoculars to watch 23 turtles at Lowell Ponds. It was found that 18 were box turtles, and five were snapping turtles.

  10. Randomized two- treatment experiment Uses a random process to assign people to treatment groups. A research project at a hospital in NY to see if a laser procedure to drill holes in the heart actually decreases chest pain. A group of 298 volunteers with severe chest pain were randomly assigned to get the laser or not. Group I – 149 patients Treatment I – Laser holes Patients with chest pain Compare pain relief Group II – 149 patients Treatment 2 – no holes

  11. Random Assignment: Put all of the patients names in a hat and draw out 149, without replacement. This group will be Group I. Flip a coin to determine whether they get laser holes or not. (Heads - laser holes) The remaing group will be the control group

  12. Bias Design that systematically favors an outcome. Selected respondent cannot be contacted or will not respond. Non-Response (Voluntary) Response Over represent people with strong opinions. Cannot be used to generalize. Confounding (lurking) The effect of one variable on another can be hidden by other variables for which no data have been obtained.

  13. Example: A drug company wants to test a new drug that is supposed to reduce the cholesterol level. Design an experiment for testing this drug in males and females ages 40 to 66 using a sample of 60, half of whom are males. To achieve blocking by gender, first separate the men and women. Label the 30 men with the numbers 1 to 30. Put the numbers in a hat and draw 15 without replacement. These men will receive the new drug. The remaining men will receive the old drug and will be the control group. Repeat this process for the women.

  14. Which of the following are true statements? I. In an experiment some treatment is intentionally forced on one group to note the response. II. In an observational study information is gathered on an already existing situation. III. Sample surveys are observational studies, not experiments Answer: I, II, and III

  15. 12. To survey the opinions of bleacher fans at Wrigley Field, a surveyor plans to select every one-hundredth fan entering the bleachers one afternoon. Will this result in a SRS of Cub fans who sit in the bleachers. a. Yes, because each bleacher fan has the same chance of being selected. b. Yes, but only if there is a single entrance to the bleachers. c. Yes, because the 99 out of 100 bleacher fans who are not selected will form a control group. d. yes, because this is an example of systematic sampling, which is a special case of SRS. e. No, because not every sample of the intended size has an equal chance of being selected. e Answer:

  16. 13. Consider the following three events, and tell the type of Bias in each. I. Although 18% of the student body are minorities, in a random sample of 20 students, 5 are minorities. II. In a survey about sexual habits, an embarrassed student deliberately gives the wrong answers. III. A surveyor mistakenly records answers to one question in the wrong space. I Sampling Error II Response Bias III Human Error Answer:

  17. In a 1927-32 Western Electric Company study on the effect of lighting on worker productivity, productivity increased with each increase in light but then also increased with every decrease in lighting. If it is assumed that the workers knew a study was in progress, what is this an example of? Answer: Placebo Effect

  18. Which of the following are true statements about blocking? I. Blocking is to experiment design as stratification is to sampling design. II. By controlling certain variables, blocking can make conclusions more specific. III. The paired comparison design is a special case of blocking. I, II, and III Answer:

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