Statistics Ways to Collect Data ­ MORE DETAILED IN YOUR CLASS NOTES

Survey  A benefit ­ you can collect a lot of information easily for a relatively  low cost A weakness ­ motivation for responding (those who are responding  might be doing so because of a strong opinion, so the sample may  not be a fair representation of the larger population)and/or lack of  response

Controlled Experiment ­ remember, control group and experimental  group A treatment is imposed/given. Concerns:  Placebo effect

Observational Study You observe, document and report.  You do not give any type of  treatment.   Often used when ethics are a concern ­ you can observe what  happens after someone is exposed to a harmful chemical, but you  cannot give them a harmful chemical to see what happens. Concerns: these are usually long term, so you can 'lose' subjects and  over time, more and more outside influences can play a role in what  you are observing.

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Ways to Interpret Data ­ MORE DETAILED IN YOUR CLASS  NOTES Measures of Central Tendency Mean Median  Mode

Measures of Dispersion Range IQR Variance and Standard Deviation

Five Number Summary Minimum Value Q1 (first quartile) Median (same as Q2) Q3 (third quartile) Maximum Value

Remember,  Population ­ you  must know all data  values. Sample ­ you know  a portion of the  entire group of data  values.  

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Normal Distribution ­

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Percentiles and the Normal Curve

All of this information  is on the percentile  handout I gave you.

1. Consider an IQ test, with a mean of 100 and a standard deviation of 15. If a student scores a 115, would percentile would that score represent?

2 An introductory psychology teacher who has taught for years has  developed a comprehensive final exam that is normally distributed with a  mean of 200 points and a standard deviation of 25 points. (a) What  percentage of the students score above 200 points? (b) What percentage of  the students score below 175 points? (c) What percentage of the students  score more than 250 points? (d) What are the percentile ranks for the three  scores 200, 175, and 250?

3. Suppose Emily is taken to the doctor for a well-baby check and it is determined that she is in the 5th percentile for height and 7th percentile for weight. What do you now know about Emily, as compared to other children her age?

4. Given a standardized test with a mean score of 78 and a standard deviation of 5.9, a student who scored in the 60th percentile could have a score of: a. 84 b. 72 c. 79 d. 76

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1. The mean is 82.75 and the standard deviation is 2.25. If the scores were normally distributed, which of the following scores would be most likely to occur? d. 77 c. 80.5 b. 87.25 a. 90

2. Given a normal distribution with a mean of 240 and a standard deviation of 32, what percent of scores would lie within the following intervals: a. 240 and 272 b. 192 and 256 c. 176 and 336 d. 160 and 320

3. The company you work for manufactures light bulbs. They advertise that the “average light bulb” can burn for 1,000 hours. Tests have shown that this is the mean length of time. The times that the lights can burn are normally distributed with a standard deviation of 200 hours. What percent of the bulbs could be expected to last 600 or fewer hours? d. 30.9 c. 6.7 b. 2.3 a. 0.6

4. On a standardized test with a normal distribution, the mean is 85 and the standard deviation is 5. If 1,200 students take the exam, approximately how many of them are expected to earn scores between 90 and 95? a. 14 b. 98 c. 163 d. 1,172

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5. In a normal distribution, x is the mean and σ is the standard deviation. If x + 0.5σ = 100 and x ­ 0.5σ = 80, what is the mean? a. 5 b. 10 c. 20 d. 90

6. A particular tire company advertises a tire that lasts for 80,000 miles. The mileage for the tires is a normal distribution with a mean of 80,000 miles, and a standard deviation of 10,000 miles. If the company produces 32,000 tires, how many of them would be expected to last between 65,000 and 100,000 miles? a. 27,212 b. 29, 120 c. 30,528 d. 31,264

7. On a standardized test with a normal distribution, the mean was 42 and the standard deviation was 2.6. Which score could be expected to occur less than 5 percent of the time? a. 50 b. 45 c. 39 d. 37

8. You manage a company that manufactures nuts and bolts. The size of the diameters of the bolts manufactured produces a normal distribution. The mean size of a certain bolt is 3 centimeters; with a standard deviation is 0.1 centimeter. Bolts that vary from the mean by more than 0.3 centimeters cannot be sold. If the company manufactures 150,000 of the 3 cm bolts, approximately how many of them cannot be sold? a. 150 b. 300 c. 15,000 d. 30,000

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9. In a normal distribution, x is the mean and σ is the standard deviation. If x + 2σ = 60, and x ­ 2σ = 40, what is the standard deviation? d. 50 c. 20 b. 10 a. 5

10. The mean age of the entering freshman class at a certain university is 18.5, with a standard deviation of 0.75 years. If the data produces a normal distribution, find. a. the percent of students who are between 19.25 and 17.75 years of age b. the number of students who could be expected to be younger than x ­ σ years of age, if the total number of incoming freshman is 1,200 students.

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A set of normally distributed student test scores has a mean of 80 and a standard deviation of 4. Determine the probability that a randomly selected score will be between 74 and 82.

The amount of time that a teenager plays video games in any given week is normally distributed. If a teenager plays video games an average of 15 hours per week, with a standard deviation of 3 hours, what is the probability of a teenager playing video games between 15 and 18 hours a week?

. In a certain school district, the ages of all new teachers hired during the last 5 years are normally distributed. Within this curve, 95.4% of the ages, centered about the mean, are between 24.6 and 37.4 years. Find the mean age and the standard deviation of the data.

From 1984 to 1995, the winning scores for a golf tournament were 276, 279, 279, 277, 278, 278, 280, 282, 285, 272, 279, and 278. Using the standard deviation for the sample, Sx, find the percent of these winning scores that fall within one standard deviation of the mean.

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The mean of a normally distributed set of data is 56, and the standard deviation is 5. In which interval do approximately 95.4% of all cases lie? (1) 46­56 (3) 51­61 (2) 46­66 (4) 56­71

In a New York City high school, a survey revealed the mean amount of cola consumed each week was 12 bottles and the standard deviation was 2.8 bottles. Assuming the survey represents a normal distribution, how many bottles of cola per week will approximately 68.2% of the students drink? (3) 9.2 to 14.8 (1) 6.4 to 12 (4) 12 to 20.4 (2) 6.4 to 17.6 The amount of ketchup dispensed from a machine at Hamburger Palace is normally distributed with a mean of 0.9 ounce and a standard deviation of 0.1 ounce. If the machine is used 500 times, approximately how many times will it be expected to dispense 1 or more ounces of ketchup? (1) 5 (3) 80 (2) 16 (4) 100

Mrs. Ramírez is a real estate broker. Last month, the sale prices of homes in her area approximated a normal distribution with a mean of $150,000 and a standard deviation of $25,000. A house had a sale price of $175,000. What is the percentile rank of its sale price, to the nearest whole number? Explain what that percentile means. Mrs. Ramírez told a customer that most of the houses sold last month had selling prices between $125,000 and $175,000. Explain why she is correct.

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The amount of juice dispensed from a machine is normally distributed with a mean of 10.50 ounces and a standard deviation of 0.75 ounce. Which interval represents the amount of juice dispensed about 68.2% of the time? (3) 9.75­11.25 (1) 9.00­12.00 (4) 10.50­11.25 (2) 9.75­10.50

Twenty high school students took an examination and received the following scores: 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73 Determine what percent of the students scored within one standard deviation of the mean. Do the results of the examination approximate a normal distribution? Justify your answer.

The national mean for verbal scores on an exam was 428 and the standard deviation was 113. Approximately what percent of those taking this test had verbal scores between 315 and 541? (3) 38.2% (1) 68.2% (4) 26.4% (2) 52.8%

On a standardized test, the distribution of scores is normal, the mean of the scores is 75, and the standard deviation is 5.8. If a student scored 83, the student’s score ranks (1) below the 75th percentile (2) between the 75th percentile and the 84th percentile (3) between the 84th percentile and the 97th percentile (4) above the 97th percentile

Battery lifetime is normally distributed for large samples. The mean lifetime is 500 days and the standard deviation is 61 days. Approximately what percent of batteries have lifetimes longer than 561 days? (3) 68% (1) 16% (4) 84% (2) 34%

The mean score on a normally distributed exam is 42 with a standard deviation of 12.1. Which score would be expected to occur less than 5% of the time? (3) 60 (1) 25 (4) 67 (2) 32

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During a particular month, a local company surveyed all its employees to determine  their travel times to work, in minutes.  The data for all 15 employees are shown  below.

25   55   40   65   29 45   59   35   25   37 52   30     8   40   55

Determine the number of employees whose travel time is within one standard  deviation of the mean.

Assume that the ages of first­year college students are normally distributed with a  mean of 19 years and standard deviation of 1 year.  To the nearest integer, find the  percentage of first­year college students who are between the ages of 18 years and  20 years, inclusive.  To the nearest integer, find the percentage of first­year college  students who are 20 years old or older.

In a study of 82 video game players, the researchers found that the ages of these  players were normally distributed, with a mean age of 17 years and a standard  deviation of 3 years.  Determine if there were 15 video game players in this study  over the age of 20.  Justify your answer.

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