Experimental Design/ Descriptive Statistics
People who get lots of vitamins by eating five or more servings of fresh fruits and vegetables each day have much lower death rates from colon cancer and lung cancer according to many observational studies. True or false: We can conclude that eating more fresh fruits and vegetables causes lower death rates from colon cancer and lung cancer. Justify your answer!
False! This is an observational study! Correlation is not causation!
(Madi to pull up Exam 2 Q1) Estimate the SD for midterm scores. Estimate the SD for final exam scores.
SD for midterm scores = About 10
SD for final scores = About 25
Yahtzee is a popular game where you roll 5 dice. A “Yahtzee” is when you roll all 5 dice with the same number of spots. What is the chance of rolling all 2's or rolling all 6's ?
.03%
A public health administrator wants to estimate the average age of Utah residents who have had Covid-19. To do this, she takes a simple random sample of 1000 Utah residents from all of those who have tested positive for Covid-19 and finds out their ages. What is the parameter?
The average age of all Utah residents who have had Covid-19.
When the sample size is under ____ , our data is _______ , and the box/population is ____________ distributed, we use the t-test
30
Quantitative
Normally
(Madi to pull up Exam 1 Q1) Approximately what percentage of Americans in the survey said they would pay at least $21 but under $61 a month on streaming services?
32%
Name a change in data that will NOT change r (the correlation coefficient)
One of the following...
shift data left or right
shift data up or right
zoom in or out (multiply/divide data)
switch x and y
I have 17 plants:
● 3 orchids
● 3 violets
● 5 tulips
● 6 foliage plants
I plan to choose 2 plants at random to put together in a decorative planter.
What's the chance that the second plant is an orchid given the first plant is a violet?
3/16
Four hundred draws will be made at random with replacement from the box with the following tickets. 1 2 5 8 You expect the sum of the draws to be ____ give or take ____
1600 give or take 54.77
If I take a simple random sample of 200 tickets from a box and the tickets in the box don’t follow the normal curve, is a test of significance still valid? Why or why not?
A significance test is still valid since it is a large simple random sample, so the Central Limit Theorem applies.
(Madi to pull up Exam 1 Q3 Hist) Find the percent of DACA beneficiaries under 5 years old.
38.35%
The average 2014 vaccination rate is 91.8 with an SD of 3.0
The average 2017 vaccination rate is 91.5 with an SD of 2.5.
The correlation coefficient is .35.
Interpret the correlation coefficient.
Fairly weak positive linear relationship
If two events can never occur at the same time, what do we call them?
Mutually exclusive
A coin is tossed 500 times. How many heads do we expect to see? Give or take how many?
250 give or take 11.18
I perform a one-tail z test and get a resulting p-value of 3.2%. Interpret this value. Don't make a conclusion of significance, tell me what the p-value means!
There is a 3.2% chance of observing what we did in our sample or more extreme (in one direction) given that our null hypothesis was true.
(Madi to pull up Exam 1 Q3 Tab) Find the percent of DACA beneficiaries between 10 and 15 years old.
22%
The average 2014 vaccination rate is 91.8 with an SD of 3.0
The average 2017 vaccination rate is 91.5 with an SD of 2.5.
If the plot 2014 rates on the x axis, and 2017 rates on the y axis, what is one point that the least mean square regression line is guaranteed to go through?
The point of averages! (91.8, 91.5)
What are the odds of rolling a 5 on a 6 sided die, drawing a king from a standard deck, and getting heads when flipping a fair coin?
(1/6) * (1/13) * (1/2)
Compare the accuracy of these two samples:
15% of adults in Salt Lake City
15% of adults in Logan
The SLC sample is more accurate
The poll randomly interviewed 1,025 women and 472 men; 47% of the women in the sample and 37% of the men in the sample said they do not get enough time to themselves. Compute the standard error used in the two-sample z-test for testing the following null hypothesis: there is no difference between the percentage of women and men who say they don’t get enough time for themselves.
2.71%
The average width of wheat seeds follows the normal curve with an average of 3.68 mm and an SD of 0.19 mm. What is the 30th percentile?
3.58
The average 2014 vaccination rate is 91.8 with an SD of 3.0
The average 2017 vaccination rate is 91.5 with an SD of 2.5.
The correlation coefficient is .35.
Find the least mean squares regression line to predict the 2017 vaccine rate using the 2014 vaccine rate.
2017 vaccine rate = .29 * 2014 vaccine rate + 64.93
Madi has 25 students in her class, but she can only take 5 of them on a field trip. 12 students in her class are freshmen, 7 are sophomores, 3 are juniors, and 3 are seniors. What is the probability that at least one senior goes on the field trip?
(You don't need to solve out your multiplication, leave in terms of fraction)
1 - (22/25) * (21/24) * (20/23) * (19/22) * (18/21)
One question asked was “Many women have better jobs and more opportunities than they did 20 years ago. Do you think women have had to give up too much in the process?” Of the 1,025 women who were asked, 492 said “Yes.” Take these 1,025 women to be an SRS of all adult women in the contiguous United States. Which of these is a correct 95% confidence interval?
48% ± 3.1%
Do you get enough time for yourself?
Yes No Totals
Men 175 297 472
Women 482 543 1025
Totals 657 840 1497
Are feelings of self-care and gender associated?
Test statistic = 12.99
Degrees of freedom = 1
p-value < 1%
Reject the null, there is evidence that self-care and gender are associated.