Biol 528 Exam 1

Given a binomial distribution with a probability of success = 0.6, what is the standard deviation after 10 trials? 0.6 * 10 10 * 0.6 * 0.4 (10 * 0.6 * 0.4)^0.5 A or B

(10 * 0.6 * 0.4)^0.5

# of Antelope Bands Cum. Freq Cumulative Prob 1 2 0.0769 2 3 0.1154 3 5 0.1923 4 10 0.3846 5 11 0.4231 6 14 0.5385 7 15 0.5769 8 17 0.6538 9 18 0.6923 The table above is a cumulative frequency of antelope bands observed. What is the probability of observing 7 or more antelope bands? Answer your question using a decimal with a zero: example: 0.XX

0.4615 Yes! think about the cumulative frequency you did on the HW 2. (1-cumulative probability of 6 bands)

# of Antelope Bands Cum. Freq Cumulative Prob 1 2 0.0769 2 3 0.1154 3 5 0.1923 4 10 0.3846 5 11 0.4231 6 14 0.5385 7 15 0.5769 8 17 0.6538 9 18 0.6923 The table above is a cumulative frequency of antelope bands observed. What is the probability of observing 7 or more antelope bands OR 2 or less antelope bands? Answer your question using a decimal with a zero, example: 0.XX

0.5769 Yes! think about the cumulative frequency you did on the HW 2- cumulative probability of 6 bands + cumulative frequency of 2 or less bands

Binomial Properties

1.The event, or trial, occurs a specified number of times (denoted as k) 2.For each event there are two mutually exclusive outcomes (success, p) (failure, q) p+q = 1 q=1-p 3.The events are independent 4.The number of times that the outcome of interest occurs in k events is designated as x. Probabilities of x designated as p(x)

Using the characteristics of the Normal Distribution answer the following question: The length of bluegill fish is normally distributed with a mean of 70mm and a standard deviation of 5mm. What percentage of bluegill fish is greater than 75mm? 34.13% 50% 68.26% 15.87%

15.87

Binomial Distribution

A probability model used with 2 possible outcomes (Discrete) Allergy medication works, or doesn't work Children w bacterial infection respond to antibiotic, or not Kittens born as male, or female Success Or Failure Number of trials defined

Which of the following are characteristics of the Normal Probability Distribution Mean Standard Deviation Asymptotic tails All of the above

All the Above

Why is it impossible to calculate a 100% confidence interval?

As confidence increases, Z continues to infinity. So there is no finite Z value for 100% confidence. The Normal Distribution is not bounded at the upper or lower end - it 'contains' infinite standard deviations. A calculation of a 100% confidence interval implies finite boundaries, and is therefore by definition of the normal distribution, an impossibility

Coefficient of Variation

C.V. is the s.d. divided by the mean and put into % terms (s.d. / Xbar) * 100 since it is in %, one can compare the variability between 2 or more groups, or years the bigger the %, the more variation

How was Normal Distribution discovered?

Discovered by Abraham de Moivre in 1733 when he was looking for a way to approximate binomial probabilities when the number of trials was large and p = 0.5. After graphing the data, he discovered a trend. his theorem was later proved for arbitrary values of p by Pierre Simon Laplace.

Point Estimate

Estimating the boundaries we expect with _____ confidence the "true" population mean to fall within

Nominal Scale or Classification Set

Events fall into a particular class or category of which there may be two or more categories

The correct equation to apply to the following problem is the Z formula for a sampling distribution: What is the probability that any randomly sampled individual mosquito fish (with a population mean of 34.29 and standard deviation of 5.49) would have a length of 40mm or larger? True False

False

Two events are independent when the occurance of the first event has an effect on the probability of the second event occuring. True False

False

The antelope band data is an example of variable measured on a continuous scale. True False

False-Correct there is not an infinite values between connected points (you can't have 1.5 antelope bands)

The Y axis of a histogram is the units of variable True False

False-The Y axis is the vertical axis and that is the frequency

Box and Whiskers Plot

Find the median Find the median of the "second half" Find the median of the "first half" Plot Q1, Q2, Q3 Draw a box around Q1- Q3 Draw whiskers to max and min 3.9, 4.1, 4.2, 4.3, 4.4, 4.4, 4.4, 4.4, 4.5, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, 5.1

Choose which term (below) best completes this sentence: As the level of confidence increases (say from 80% to 99%), the interval range __________. Decreases or gets smaller The range stays the same because the SE does not change if the population does not change Increases or gets larger It depends on the sample mean

Increase or gets larger: The Confidence interval is the mean + or - (Z*(SE)) Where Z* is the probability of the Z that corresponds with your confidence level. The higher the confidence the higher the Z* and therefore the interval size is larger.

Binomial

K=The event occurred a specified number of time Ex: A coin flipped 5 times, K=5 P= Probability of the outcome of interest occurring or success Q= Probability of failure: P-1 5!= 5*4*3*2*1

Parameters from the Law (Binomial)

Mean= K*P Variance = k * p * q Standard Deviation = (k * p * q)^.5

Which of the following is NOT a measure of dispersion: Median Variance Range Standard Deviation

Median

If you are examining the variable, "Lobster Sex (male or female)" which measure of central tendency would you use to best describe the center of the distribution? Mean Median Mode Variance

Mode Lobster gender is a categorical variable, you would use mode to describe the most frequently occuring category - male or female

Multiplication Rule "and" Rule

Pr (A and B) = Pr(A)*Pr(B) Ex: Probability of choosing a queen of hearts (4 / 52) * (13 / 52) = 52 / 2704 = 1 / 52

Addition Rule "OR" rule (Mutually Exclusive)

Pr (A or B) = Pr(A) + Pr(B) Ex: Probability of picking student A or B (1 / 100) + (1 / 100) = 2 / 100

Addition Rule (Dependence)

Pr (A or B) = Pr(A) + Pr(B) - Pr(A)*Pr(B) Pr(drawing a Queen or a Heart)= Pr(Queen) + Pr(Heart) - Pr(Queen)*Pr(Heart)= (4 / 52) + (13 / 52) - (4 / 52) * (13 / 52)= 17 / 52 - 1 /52 = 16 / 52 = 30.77%

As the sample size increases, the standard error of the mean gets: Larger Smaller

Smaller: As the sample size gets larger, the SE of the mean gets smaller, and therefore our estimates become more precise.

Which measure of dispersion is the most useful measure to describe the average dispersion of the sample? Standard Deviation Range Variance Either A or B

Standard Deviation-Yes, because the standard deviation is in the units of the measured variable it is the most useful measure of dispersion

If the measures of central tendancy are not all equal, this tells us....

The data is skewed

Z Score

The number of standard deviations FROM THE MEAN an observation lies

Conditional Probability

The probability that Event A occurs, given that Event B has occurred

Ordinal (Ranking) Scale

This is where less than and greater than come into play, or not improved, somewhat improved or greatly improved

A property of the normal probability distribution is that the distribution is completely defined by the mean (mu ) and standard deviation (sigma ). True False

True

T/F When k is fairly large and p is not too near 0 or 1, the binomial distribution becomes approximately a normal distribution. True False

True

The correct equation to apply to the following problem is the Z formula for a sampling distribution: What is the probability that a random sample of 10 mosquito fish (with a population mean of 34.29 and standard deviation of 5.49) would have a mean length of 40mm or larger? True False

True

A Statistic is from a Sample and a Parameter is from a Population True False

True - when you draw a sample from a population you will calculate statistics; but if you have data from the entire population your Mean, etc. is a parameter

The Central Limit Theorem states that even if a continuously measured variable is not normally distributed, the distribution of repeated sample means will be normally distributed. True False

True: In the video I show the example of city populations which is not normally distributed but if taken multiple samples, get the mean from each sample, plot the distribution of sample means THAT distribution is normally distributed.

One of the conditions of using or applying the binomial distribution is that the events must occur a specific amount of times. True False

True: k = a value. Take the kittens example, tossing a coin, each of these examples were given a specific # of events. The cat had 6 kittens, the coin was tossed 2 times.

Which measure of dispersion is in the squared units of the variable? deviation range variance standard deviation

Variance

Which of the following is NOT a measure of central tendency Mean Variance Median Mode

Variance

Type 2 Error

When you fail to reject the null hypothesis when you should have done so

Normal Distribution

based upon mean and standard deviation like the Binomial, there exists a never ending number of distributions

Interquartile Range

measures the range of the middle half of the data Q3 - Q1 eliminates extreme values

Fill in the blanks in the formula for the mean: xbar= Sigma*X/ ______

n

Relative Measures of Dispersion

s.d.'s are in measurement terms; i.e. quarts, mm, people, lobsters, degrees, etc. cannot compare people to lobsters using s.d.'s because of the units of measure; most people are bigger than rats

When constructing a confidence interval there are 2 components that will have a great impact on the size of the interval (upper limit - lower limit). What are these 2 factors? sample mean and confidence level sample standard deviation and confidence level sample mean and sample size sample size and confidence level

sample size and confidence level: as the sample size increases the standard error will become smaller and as the confidence level increases the value of Z will increase

Sum of Squares

squaring eliminates the negatives and the sum is a nonzero positive value often becomes a really big number

Which measure of dispersion is in the units of the variable? mean median sum of squares standard deviation

standard deviation is the square root of variance

Characteristics of Normal Distribution

symmetrical area under the curve sums to 1.0 X can take values; -∞ to ∞ asymptotic tails

Variance

the n-1 allows for sampling error and makes the statistic unbiased the "average" squared distance of all observations from the mean

Standard Deviation

the square root of the variance same scale as the mean! it is a measure of the "average" amount by which each observation in a data set differs from the mean

Conditionally Dependent

two events, X and Y, are conditionally dependent if the outcome of Y depends on X, or X depends on Y

Independent

two events, X and Y, are independent if the outcome of Y does not influence the outcome of X Ex: winning numbers on the roulette wheel

Mutually Exclusive

two events, X and Y, are mutually exclusive if the occurrence of one prevents the occurrence of the other. Also, the events can not occur at the same time. Ex: Sex, Male or Female or Rolling dice (you cant role a 2 AND a 6 at the same time)

Type 1 Error

when you reject the null hypothesis when you should not have done so.