Vocab
The Federal Aviation Administration tells airlines to assume that passengers weigh an average of 190 pounds (including clothing and carry-on baggage), with a standard deviation of 35 pounds. A commuter plane carries 20 passengers. What is the probability that the total weight of the passengers exceeds 4000 pounds?
What is the population?
What is the sample?
Population- all people traveling by plane in the U.S.
Sample- the 20 passengers on the airplane
The number of blue marbles in a bag if 20% of the marbles are red, 5% are white, 30% are green, 15% are black, and the rest are blue. There are 40 marbles total
What is 12 marbles
What would the z* be for 80%
What would the t* be if the sample was 23?
z*=1.282
t*= 1.321
If you got a t-score of 1.97, the test is 2-sided, and you have a sample of 10. Can you reject the null hypothesis if alpha=0.05?
No 1.97<2.262, so you fail to reject the null
We draw an SRS of size n from a Normal population that has a known mean μ and known standard deviation σ. We want to test if our sample mean is significantly different from the true population mean.
z-test
Define Statistic
a number that can be computed from the sample data
One year, many college-bound high school seniors in the U.S. took the Scholastic Aptitude Test (SAT). For the verbal portion of this test, the mean was 425 and the standard deviation was 110. Based on this information is the probability that a student would score between 350 and 550?
What is 62.45%
If I increase the sample mean, then the margin of error will (increase/decrease/stay the same)
stay the same
You run an experiment to see if your sample is significantly shorter than the US population. Your sample has a mean height of 65.9in. The population has a mean height of 67.1in and a standard deviation of 2.1in. Is your sample significantly shorter at the 0.05 level? (n=16)
Yes, p=0.0111 therefore it is statistically significant
A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 70 on the test. The six students get scores of 62, 92, 75, 68, 83, and 95. Can the professor have 90 percent confidence that the mean score for the class on the test would be above 70?
t-test
When you send out a survey to 100 emails randomly, you will receive a ___________ sample which is prone to __________ bias
voluntary response; non-response
10%
The margin of error for a 90% confidence interval where the sample mean is 5.4, the sample standard deviation is 1.1, and the sample is 16 individuals
0.4821
The time it takes to download a video game is normally distributed with µ=2 hrs and σ=1hr. Dave believes it takes longer than 2 hrs to download a video game and so he randomly downloads 20 video games and finds the average time it takes to download a video game to be 2 hours and 30 minutes. What is the null hypothesis, alternative hypothesis, P-value, and statistical significance of the P-value at a significance level of α=.01
Ho: µ=2hrs, Ha: µ>2hrs, P=.0127, Not statistically significant and can not reject null hypothesis
We draw an SRS size n from a large population having unknown mean μ, with a confidence interval C, we want to estimate the mean of this population-based off the sample mean and standard deviation
T confidence interval
The explanatory variables are often called ________
Factors
The probability of rolling a 6-sided die twice and getting a sum of 2, 3, 7, or 10
What is .33?
The approximate sample size of a study of the time it takes hippos to walk up a hill if there is a 95% confidence interval of 7 minutes to 10 minutes with a standard deviation of σ=500 seconds
What is 119 hippos?
We have the potato yield from 12 different farms. We know that the standard potato yield for the given variety is µ=20. x = [21.5, 24.5, 18.5, 17.2, 14.5, 23.2, 22.1, 20.5, 19.4, 18.1, 24.1, 18.5]. Test if the potato yield from these farms is significantly better than the standard yield at the 0.05 level.
t=0.201, not significant, fail to reject null