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# Statistics: observed value, imperial rule, bar graph, random sample, sampling methods

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1-Find the percentile for the observed value in the following situation:

a. GRE score of 450 (mean = 497, s.d. = 16)
b. Stanford - Binet IQ score of 92 ( mean 100, s.d. =16)
c. Woman's height of 68 inches (mean=65 inches, s.d. = 2.5 inches)

2- Use imperial rule to specify the ranges into which 68%, 95%, and 97% of Stanford - Binet IQ scores fall. (Recall the mean is 100 and the standard deviation is 16).

3- An article reported on a "telephone survey of 2600 parents, students, teachers, employers, and college professors" in which people were asked the question, "Does a high school diploma mean that a student has at least learned the basic? Results were as follow:

Professor Employers Parents Teachers Students

Yes 22% 35% 62% 73% 77%
NO 76% 63% 32% 26% 22%

a. The article noted that "there seems to be a disconnect between the producers [Parents, teachers, students] and the consumers [professor, employers] of high school graduates in the U.S. Create a bar graph from this study that
emphasizes this feature of the data.
b. Create a bar graph that deemphasizes that.

4- For each of the following situation, state which type of sampling plan was used. Explain whether you think the sampling plan would result in a biased sample.

a. To survey the opinions of its customers, an airline company made a list of all it flights and randomly selected 25 flights. All of the passengers on those flights were asked to fill out a survey.
b. A pollster interested in opinions on gun control divided a city into city blocks, then surveyed the third house to the west of south east corner of each block. If the house was divided into apartments, the westernmost ground floor apartment was selected. The pollster conducted the survey during the day, but left a notice for those who were not home to phone her so she could interview them.
c. To learn how its employee felt about higher student fees imposed by the legislature, a university divided employees into three categories: staff, faculty, and student employees. A random sample was selected from each group and
they were telephoned and asked for their opinions.
d. A large variety store wanted to know if consumers would be willing to pay slightly higher prices to have computers available throughout the store to help them locate items. The store posted an interviewer at the door and told her
to collect a sample of 100 opinions by asking the next person who comes in the door each time she had finished an interview.

5- In the March 8, 1994, edition of the Scotsman, a news paper published in Edinburgh Scotland , a headline read, "Reform study find fear over schools"
The article described a survey of 200 parents who had been asked about proposed education reforms and indicated and most parents felt uninformed and thought the reforms would be costly and unnecessary. The report did not clarify whether a random sample was chosen, but make that assumption in answering the following questions.

a. What is the margin of error for this survey?
b. It was reported that "about 80 percent added that they were satisfied with the current education set-up in Scotland". What is the range of values that almost certainly covers the percentage of the population of parents who were satisfied
c. The article quoted Lord James Douglas Hamilton, the Scottish education Minister, as saying "if you took a similar poll in two years' time, you would have different result" comment on this statement.

6- An article in Sacramento Bee was titled "College freshmen show conservative side" and reported the result of fall 1997 survey "based on response from a representative sample 252,082 full time freshmen at 464 two and four year colleges and universities nationwide". The article did not explain how the schools or students were selected.

a. For this survey explain what a unit is, what the population is, and what the sample is?
b. Assuming a random sample of students was selected at each of the 464 schools, what type of sample was used in this survey? Explain
c. Now assume that the 464 schools were randomly selected from all eligible colleges and universities and that all first year students at the schools were surveyed. Explain what type of sample was used in the survey.
d. Why would one of the two sampling methods described in part b and c have been simpler to implement than a simple random sample of all first year college student in the U.S?

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