Experimental Design & Normal Distributions
Are Normal distributions formatted into 3 standard deviations ?
1 standard deviation from the mean is 68% 2 standard deviations from the mean is 95% 3 standard deviations from the mean is 99.7%
An experiment was done by medical researches to determine the association between drinking caffeine and severity of lung cancer. Results showed that there was a high association between the two variables. Which of the following could be a potential confounding variable in the experiment. 1. Smoking 2. Medical Researchers 3. Caffeine Consumption 4. Lung Cancer 5. None of these are potential confounding variables
1. Smoking A confounding variable is one that could potentially have an effect on both the independent and dependent variables in a study. In this case, it is possible that there is an association between smoking and caffeine as well as smoking and lung cancer.
A researcher wants to randomly assign participants to a treatment and control group. Which of the following approaches ensures that the treatment assignment is random? 1. Assigning the treatment based on who needs it the most. 2. Flipping a coin. 3. Obtaining nationally representative sample for both. 4. Assigning the treatment by gender.
2. Flipping a coin. Because the coin flip ensures that no background variables influence treatment assignment whereas the other examples either have nothing to do with random assignment or completely contradict the purpose of random assignment.
Of the following example, which best describes quantitative data? 1. A student's least favorite sport. 2. Temperature measurements of water in degrees Fahrenheit. 3. The softness of a chair. 4. College grade level-freshman, sophomore, junior, or senior. 5. A child's gender.
2. Temperature measurements of water in degrees Fahrenheit. Because measuring the temperature of water in degrees Fahrenheit is a numerical piece of information.
A study finds that caffeine intake has a strong positive correlation with grades for college students. In other words, on average, the more caffeine intake a student has, the higher a grade the student gets. Which of the following could potentially be a confounding variable in this experiment? 1. The caffeine intake of students 2. The amount of coffee that each student drinks 3. Amount of sleep a student gets each night 4. The grade a students receives 5. The amount of soda that each student consumes
3. Amount of sleep a student gets each night It is possible that the amount of sleep a student gets is related to caffeine intake, which in turn affects the grade a student receives on a test or assignment.
The lifespans of zebras in a particular zoo are normally distributed. The average zebra lives 20.5 years; the standard deviation is 3.9 years. What is the probability of a zebra living between 16.6 and 24.4 years. ( hint use empirical rule )
8.8 ,12.7, 16.6, 20.5, 24.4, 28.3 , 32.2 16.6 - 24.4 is 1 standard deviation from the mean so the probability of a zebra living between 16.6 and 24.4 is 68%
What two pieces of data does Normal distributions have?
A mean and standard deviations
A set of biology exam scores are normally distributed with a mean of 60 points and a standard deviation of 66 points. Antoaneta got a score of 51 points on the exam. What proportion of exam scores are higher than Antoaneta's score?
Antoaneta's score is 51 − 60 = − 9 relative to the mean. -9/ 6 = -1.5 standard deviations relative to the mean. This is Antoaneta's z-score. Want to find the proportion of exam scores above a z-score of −1.5 Looking up −1.5 on the z-table, we see that 0.0668, of exam scores are below Antoaneta's score If 0.0668 of exam scores are below Antoaneta's score 1 - 0.668 = 0.9332 0.9332 of exam scores are higher than Antoaneta's score.
The heights of the same variety of pine tree are normally distributed. The mean height is μ=33m and the standard deviation is σ = 3m Which of the following fit the data A. 21, 24, 27, 30 , 33 , 36, 39 B. 24, 27, 30 , 33 , 36 , 39 , 42 C. 27, 29 , 31 , 33 , 35 , 37 , 39 D. 24, 25 ,26 , 27 , 28 , 29 , 30
B. 24, 27, 30 , 33 , 36 , 39 , 42
What is a Normal Distribution?
Bell curve that shows the spread of data presented
A college dean is interested in whether students feel their campus has an appropriate academic setting. The dean sends out the survey to all students at the campus. The college dean is attempting to conduct a(n)
Census Because it involves the entire population being surveyed.
You and your friend want to test the effect of different brands of fertilizer on sunflower height. One group receives no fertilizer during the course of the experiment. Which group is this?
Control group Because the sunflowers getting no fertilizer do not receive the treatment, it is the control group.
You and your classmate want to test the effect of food coloring on plant color. One of the groups in the experiment receives dye-free water. Which group is this?
Control group Because the flowers getting no dye do not receive the treatment, it is the control group.
What type of sample was used in the following scenario: Brad wants to know about the shopping habits of teenagers. He goes to the local mall and every time he sees a teenager he asks them to fill out his survey, He spends one hour collecting responses on the top floor of the mall and one hour collecting responses on the bottom floor of the mall.
Convenience Sample Because the sample is drawn from a population that is close, readily available, and convenient. The sample does not represent the shopping behaviors of all teenagers.
A study is trying to determine if a particular medication (Y) is effective in weight loss. Patients participating in the study were randomly assigned to groups A, B, C, D, or E. Group A will receive one dose of Y, Group B will receive two doses of Y, Group C will receive three doses of Y, Group D will receive four doses of Y, and Group E will serve as the control group. Which group will be receiving the placebo (a sugar pill)?
Group E Because the control group in an experiment typically receives placebo treatments.
What is the main difference between an observational study and an experiment?
In an experiment, some type of treatment is imposed upon subjects, while in an observational study no treatments are imposed.
What is a Z score ?
Shows by how many standard deviations a score is above or below the mean.
What does a Z table show?
Shows z-scores in the margins and area under the curve to the left of the z-score
1 standard deviation from the mean is 68% 2 standard deviations from the mean is 95% 3 standard deviations from the mean is 99.7% Is also known as?
The Empirical Rule
Why is the mean and standard deviation relevant in a normal distribution?
The Mean (μ) is needed to know the overall average and the Standard Deviation (σ) is needed to know the spread from the mean. Not only does the Standard Deviation tell the spread from the mean but whether or not a certain pice of data being asked for is above or below the mean.
A set of average city temperatures in April are normally distributed with a mean of 19.7C and a standard deviation of 2C. The average temperature of Kabul is 15C What proportion of average city temperatures are lower than that of Kabul?
The average temperature of Kabul is 15 − 19.7 = −4.7 relative to the mean. This is − 4.72/2 = −2.35 standard deviations relative to the mean. This is Kabul's z-score. We want to find the proportion of average temperatures below a z-score of −2.35 Lookterm-20ing up −2.35 on the z table we see that 0.0094, 0.0094 of average temperatures are below that of Kabul
A certain variety of pine tree has a mean trunk diameter of μ= 150 cm standard deviation of σ = 30 cm A certain section of a forest has 500 of these trees. Approximately how many of these trees have a diameter smaller than 120 cm?
The diameter of 120 cm is one standard deviation below the mean. Add the percentages in the shaded area. 0.15% + 2.35% + 13.5% = 16% About 16% of these trees have a diameter smaller than 120 cm We need to find how many trees 16% of 500 is. 0.16 x 500 = 80 About 80 trees have a diameter smaller than 120 cm
A certain variety of pine tree has a mean trunk diameter of μ= 150 cm standard deviation of σ = 30 cm Approximately what percent of these trees have a diameter greater than 210 cm?
The diameter of 210cm is two standard deviations above the mean. Add the percentages in the shaded area. 2.35% + 0.15% = 2.5% About 2.5% of these trees have a diameter greater than 210cm
A major chocolate company wants to test the effects of adding more sugar to their standard chocolate bar to see if customers enjoy it more. They select 10 subjects to randomly participate in a taste test. They bring in samples of their original product, which is sold in tiny squares that says the company's name on them, and samples of the increased-sugar versions, which are plain chocolate squares of the same size. The company asked participants to taste both chocolate and rank how much they like them on a scale of 1 to 10. Which of the following represents a possible source of bias in the study?
The original recipe has the company's name on it , but the new sample does not. The presences of the company;s name on the original sample may be a source of bias because people already have preexisting opinions about the brand, they may rate that chocolate as better or worse based on those opinions rather than flavors.
A drug company wants to test whether its medication reduces cancer risk. Assuming the company conducts and experiment in which participants are randomly assigned to treatment an control groups, what would the appropriate control group look like?
Tterm-20hose assigned to the control take a sugar pill. The only thing you want to vary across groups when you're conducting an experiment is the treatment. Since taking pills is a part of taking medication (the treatment), medical experiments often employ something called a placebo-controlled study where outcomes for those who are randomly assigned to take the medication are compared to outcomes for those who are randomly assigned to take a sugar pill. The sugar pill is expected to have no effect, so it serves as a useful baseline to compare the treatment to.
