Sampling Distributions
Where is a sampling distribution centered around?
population parameter
Where is the bootstrap distribution centered?
Around the sample statistic
What does a confidence interval estimate?
The population parameter
Which symbol is used when writing the null hypothesis?
H0: parameter = hypothesized value
The Pew Research Center conducted a survey in 2025 about relationships1. Out of the 543 U.S. adults married or living with a partner, 210 of them reported they were very satisfied with the way household chores were divided.
What's the population? What's the sample?
1.All U.S. adults married or living with a partner in 2025
2. 543 U.S. adults married or living with a partner in 2025
A bootstrap sample
What formula can you use to find the 95% confidence interval?
statstic +/- 2*SE
Where will a randomization test be centered around?
p0 value (hypothesized value)
Is there a difference between population and parameter? Why or why not?
population- the entire group you care about
parameter- A numerical summary that describes the population
Describe the distribution of a bootstrap distribution.
Unimodal and symmetric
If we were to create a 99% confidence interval for a data, would the interval be narrower or wider than the 90% confidence interval?
It would be wider. As the confidence level increases, the width of a confidence interval increases.
What does a small p-value indicate?
Strong evidence against the null hypothesis
Write the symbols for the following numerical sumarry:
1. Parameter mean
2. Parameter proportion
3. Statistic mean
4. Statistic proportion
1. u
2. p
3. x(bar)
4. p(hat)
we create a bootstrap distribution in StatKey with 200 bootstrap samples. Provide an estimate of a 90% bootstrap confidence interval.
This is found by finding roughly the end points of the middle 180 of dots (200*0.9 = 180, cut 10 off the top and 10 off the bottom).
A survey asking questions about marijuana usage was sent to 850 college students in 2014. Out of the 850 students, 323 of them reported using marijuana in the past 12 months. A bootstrap distribution was simulated in StatKey and the standard error was found to be 0.017. Compute a 95% bootstrap confidence interval
2*0.017 = 0.034
0.38 – 0.034 = 0.346
0.38 + 0.034 = 0.414
95% confidence interval: [0.346, 0.414]
Students were randomly assigned to take one of two exam versions: one starting with a difficult question and one starting with an easy question. After completing the same exam (just in different orders), their scores out of 100 were recorded.
Research Question: Is the population mean score higher for exam with simple first question than exam with difficult first question?
What are the appropriate hypothesis statements to answer the research question?
H0: μS – μD = 0 or μS = μD
HA: μS – μD > 0 or μS > μD
If we increased the sample size to 50 instead of 40, would the standard error of the sampling distribution increase, decrease, or stay the same?
The standard error would decrease because the variability in the sampling distribution decreases as sample size increases.
A random sample of 80 Iowa apartments had an average monthly rent of $3165 dollars.
Describe how you would create a bootstrap statistic using cards.
Get 80 cards (match the sample size). Write the monthly rent for each of the 80 apartments in the sample on the cards (data).Randomly choose a card and record the result.Replace the card.Repeat until there are 80 results (matching the original sample size).Compute the mean (bootstrap statistic).
The U.S. conducted a survey in 2017 which included a question about how much time they spent alone while awake. Consider a random sample of 1,423 U.S. adults aged 60+. The sample mean time they spent alone while awake was 421 minutes. Interpret the 95% bootstrap confidence interval that was found to be [381, 461].
We are 95% confident the population mean time spent alone while awake is between 381 and 461 minutes.
How do you interpret a p-value?
p-value = The probability of getting an observed statistic equal to or more extreme as we did IF THE NULL HYPOTHESIS IS TRUE