Data Analysis
Nope. It does seem that taller students have bigger feet but correlation NEVER implies causation. You must conduct an experiment to determine causation.
I have the option of picking a 95% confidence interval or a 99% confidence interval. Which confidence interval has a higher margin of error?
What is X? What is Y? HINT: Think ___ variable.
Ms. Rosenbaum advertises that 85% of her flower seeds will germinate (grow). Suppose that the company's claim is true. Armani buys a packet with 20 flower seeds from Ms. Rosenbaum and plants them in his garden. Let X=the number of seeds that germinate. This is known as a ________ distribution.
Each person in a simple random sample of 2,000 received a survey, and 317 people returned their survey. What is the name of this bias?
Suppose the correlation between two variables is r = .28.
What will the new correlation be if .17 is added to all values of the x-variable?
r = 0.28. Correlation isn't changed when you add a constant to every value of a variable.
Our 95% Confidence Interval for Delice's population mean was (230.80,250.80). How do we interpret this interval?
Exactly 10% of the students at Bronx Latin are left handed. Select students at random from the school, one at a time, until you find one who is left-handed. Let V=the number of students chosen. This is known as a _______ distribution.
If ten executives have salaries of $80,000, six have salaries of $75,000, and three have salaries of $70,000, what is the median salary?
Jessica is volunteering for opinion poll and calls residential telephone numbers at random. Only 20% of the calls reach a live person. You watch the random digit dialing machine make 15 calls. Let X=the number of calls that reach a live person. Find and interpret the mean of X.
When making 15 random phone calls, we expect 15*0.2 = 3 people to pick up on average.
Note: Stratification is used in observational studies to the same effect.
Consider a data set of positive values, at least two of which are not equal. Which of the following sample statistics will be changed when each value in this data set is multiplied by a constant whose absolute value is greater than 1?
I. The mean
II. The median
III. The standard deviation
What is the formula for calculating a confidence interval for a population mean?
Exercise physiologists are investigating the relationship between lean body mass (in kilograms) and the resting metabolic rate (in calories per day) in sedentary males. They find:
Coef StDev T P
constant 264.0 276.9 0.95 0.363
Mass 22.563 6.360 3.55 0.005
S = 144.9 R-sq = 55.7% R-sq (adj) = 51.3%
What is the appropriate interpretation for the value of the slope of the regression line?
To start her old snow blower, Ms. Nelson has to pull a cord and hope for some luck. On any particular pull, the mower has 20% chance of starting. What is the probability of it starting in exactly three pulls?
Alternatively:
p (X = 3) = (0.2)(0.8)^2
In a certain game, a fair die is rolled and a player gains 20 points if the die shows a “6.” If the die does not show a “6,” the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player?
For 100 rolls, E(X) = 0.83*100 = 83.
Using the most commonly accepted definition of outliers, a set has five outliers. If every value of the set is increased by 20 percent, how many outliers will there now be?
A large company is considering opening a franchise in St. Louis and wants to estimate the mean household income for the area using a simple random sample of households. Based on information from a pilot study, the company assumes that the standard deviation of household incomes is σ = $7,200. What is the least number of households that should be surveyed to obtain an estimate that is within $200 of the true mean household income with 95 percent confidence?
HINT: When estimating sample sizes for means, use a z-score instead of a t-score because we don't have the degrees of freedom.
At least 4976 households.
Solve the equation for n:z * sigma / sq. root (n) <= ME
Using our calculators, we get z = 1.96, sigma = $7,200 and ME = $200
(1.96) * $7,200 /sq. root (n) <= $200
$7,200 / sq. root (n) <= $102
$7,200 <= $102 * sq. root (n)
70.5 <= sq. root (n)
n >= 4976
What could be the least squares regression line?
A. y = -5.0 + 3.0x
B. y = 3.0x
C. y = 8.5 + 0.3x
A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds.
Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation of 10 pounds. If the weights of individual passengers are independent, what is the probability that a group of four adult male passengers will exceed the acceptable weight limit of 800 pounds?
First, I need to find my combined mean and standard deviation for four adults.
New mean: 190 * 4 = 760
New st. dev: sq. root of (10^2 *4) = 20
P(X > 800) = normalcdf(lower: 800, upper: 99999, mean: 760, st. dev: 20) = 0.0228
At JFK Terminal 5, all bags entering the terminal must be screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material?
P(Illegal | Trigger) = P (Illegal & Trigger) / P (Trigger)
P(Illegal | Trigger) = [0.001* 0.97] / [(0.97*0.001) + (0.15*0.999)] = 0.0064
Let's make a chart:
P(Legal) = 0.999
P(Trigger | Legal) = 0.15
P (No Trigger | Legal) = 0.85
P(Illegal) = 0.001
P (Trigger | Illegal) = 0.97
P (No Trigger | Illegal) = 0.03