Single Variable Data
Z score of 1.8 means...
The value is 1.8 standard deviations away from the mean.
What does LSRL stand for?
Least Square Regression Line
It doesn't represent the who population, leading to biased results and limited generalizability.
What calculator function should be use for P(X=n)?
binompdf or geometpdf
What is the difference between p̂ and p.
P is the population proportion, and p̂ is the sample proportion.
If the mean of a distribution is 700, and the media is 500, what is the shape of the distribution? Systematic, skewed left, skewed right, or normal.
Skewed Right
What is the correlation coefficient?
Measures the strength and direction of a linear relationship between two quantitative data.
Cluster: Population split into clusters (groups), select X number of groups
Stratified: Population split into groups of similar characteristics, select X number of people in every group.
Systematic: Selecting samples from a random starting point with a fixed periodic interval.
Interpret a 95% confidence interval for the mean number of licks to get to the center of a Tootsie Pop, which is (317.64, 394.56).
We are 95% confident that they true mean number of licks to get ot the center of a Tootsie Pop is 317.64 to 394.56.
When do you reject the null hypothesis?
Summary Statistics for weekly payroll of a small company:
Mean: $700; Median: $500; Range: $1200; Standard Deviation: $400
What are new summary Statistics if every employee gets $50 raise.
Range and Standard Deviation stay the same. New mean is $750 and the new median is $550
The predicted cost of a car from the age of the car is shown by equation (predicted cost = 3785.03 + 1261.20(age of car)). Interpret the slope.
The predicted cost of the car increases by $1261.20 for each year the car exists.
What is the difference between bias and variability.
Variability is whether or not the measured data collected is consistent and bias is whether or not the data is accurate.
What are the chances less than or equal to 2 spades are selected in a deck of cards out of 10 cards selected? Assume conditions are met.
0.5256
binomcdf(T=10, p=.25, X=2)
County Health department has concerns about the chlorine level of 0.4% mg/mL at a local water park increasing at unsafe level. The water department tests the hypothesis that the local water park's chlorine proportions have remained the same.
Ho: p=0.004
Ha: p ≠ 0.004
What is a type 1 error?
Type 1: Ha, but Ho
We reject the null hypothesis, but we shouldn't have.
We conclude that the chlorine levels have not remained the same, but it hasn't.
Acidity of pH of rainfall is described by a normal distribution with a mean of 4.9 and standard deviation of 0.6. What is the percentage of storms product rain with pH over six?
P(X>6)=P(Z>1.83)
0.0336= 3.36%
The predicted tuition = 6439.95 + 326.08(years since 1990) and the actual cost in 1994 was $7500. Interpret the residual.
Residual = -244.27
The LSRL overestimates the actual tuition by $244.27 four years after 1990.
A researcher is testing the effect on a new fertilizer on crop growth. He marks 30 plots in a field, splits the plots in half, and randomly assigns the new fertilizer to one half of the plot and the old fertilizer to the other half. What kind of design is this?
Matched pairs experiment
In a survey of 1000 television viewers, 40% said they watch network new programs. For a 90% confidence level, the margin of error for this estimate is 2.5%. If we want to be 95% confident, how will the margin of error change?
THe margin of error will be larger since more confidence requires a wider interval.
When data from a random sample is given, what should you do to see if the conditions have been met?
Plug into the calculator and see if the box plot or histogram is approximately normal. Also make sure that the sample is less than 10% of the population and also randomly selected.
A normal model describes the fuel efficiency of cars currently registered in VA. The mean is 24 mpg with a standard deviation of 6. What is the fuel efficiency of the worst 20% of cars?
18.96 mpg
Time (hrs): 0 1 2 3 4 5 6
# of ppl paying attention: 80 68 62 50 48 32 21
Create an LSRL.
Predicted # of people paying attention = 79.75 - 9.39 (time)
1) A survey about job satisfaction for school employees is given by selecting on department at random.
2) A survey is given to 20 students, and 15 return it.
3) TV news surveys where viewers are asked to call in about an issue.
1) Undercoverage
2) Non response
3) Voluntary response
In May 2002, the Gallup Poll asked 537 randomly sampled adults in the United States the question “Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country today?” Of these, 53% answered “fairly”. The researcher wants to estimate a percentage of adults in the United States who believe the death penalty is applied fairly to within + 5%, with 90% confidence. How many adults should they sample?
~270 adults
According to Mars, Incorporated, the makes of M&M's, there are supposed to be 20% orange in a bag. The bag of 122 that you just opened had only 21 orange ones. Does this contradict the company's 20% claim? Assume conditions are met.
p= 0.41.
Since our p-value of 0.41 is greater than α=0.05, we fail to reject the null hypothesis. There is no statistically significant evidence that the proportion of orange M&M's is not 20%