Sampling Distribution Basics
A value that describes some characteristic of a sample is called a...
Statistic
What is the variable used for the sample proportion?
^
p
(p-hat)
The mean SAT score for the state of Colorado (μC) is 1,201 and for Utah (μU) is 1,238. For a sampling distribution of μC - μU, what is the mean of the sampling distribution with sample sizes of 100?
-37
A field of daisies has a mean daisy height of 14 inches and a standard deviation of 2 inches. Can it be said that the shape of the sampling distribution (n=20) is approximately normal? Why or why not?
No, because n=20 is less than 30 and the shape of the population distribution is unknown.
A value that describes some characteristic of a population is called a...
Parameter
23% of students at CGHS play a sport. What would be the standard deviation of sampling distribution of samples of 10 students at CGHS?
(Round to three decimal points)
0.133
The mean SAT score for the state of Colorado (μC) is 1,201 with and for Utah (μU) is 1,238.
σC = 57
σU = 45
For a sampling distribution of μC - μU, what is the standard deviation of the sampling distribution with sample sizes of 100?
7.262
What statistic of a sampling distribution is most likely to be impacted by a sampling method without an element of randomness?
Mean
What is the variable used to represent the sample size?
n
The mean MPG of a car in Denver is 21.4 with a 7.1 standard deviation. What is the probability that a random sample of 60 cars in Denver has a mean greater than 23?
~0.040
When asked to find the probability that a sample proportion of Population A is greater than a sample proportion of Population B (with sampling distribution μpA - pB), what values would you put into the "Lower" and "Upper" fields in NormalCDF?
Lower: 0
Upper: 1
There are 327 raccoons in Northfield. What is the largest possible sample size of Northfield raccoons that allows us to model the standard deviation of the sampling distribution?
32
If a basketball player has averaged 10 points per game with a standard deviation of 2 over the course of their career, and then scored exactly 21 points per game over the last five games, how would you characterize the sample distribution of the last five games in terms of accuracy and precision?
Low accuracy, high precision
A population has a standard deviation of 462 and a sampling distribution standard deviation of 66. What is the sample size of the samples used to compile the sampling distribution?
49
The proportion of teens who choose cheddar as their favorite type of cheese is 0.35, and the proportion of adults who choose cheddar as their favorite type of cheese is 0.21. What is the probability that in a sample of 40 teens and 95 adults, it is found that more adults chose cheddar as their favorite cheese than teens?
~0.052
21 percent of kids in Denver have library cards. What is the smallest possible sample size of Denver kids that will allow for the sampling distribution of the sample proportion to be assumed approximately normal?
48
How would a sampling distribution for a normal population change if n increases from 40 to 80, and all else stays the same? Describe how center/spread/shape would increase, decrease, or stay the same.
Center stays the same
Spread decreases
Shape stays the same (normal)
71% of Denver high school students get accepted into at least one Colorado college. What is the probability that a random sample of 360 Denver high school students has 100 or more students who did not get accepted into any Colorado colleges?
~0.695
The mean time it takes a NASA rocket to reach orbit is 455 seconds with a standard deviation of 89 seconds, and the mean time it takes a SpaceX rocket to reach orbit is 292 seconds with a standard deviation of 16 seconds. Both distributions are normal. What is the probability that the next SpaceX rocket reaches orbit at least 3 minutes faster than the next NASA rocket?
~0.425
A pretzel company has two factory locations: Minneapolis and Detroit. The Minneapolis factory has a left skewed distribution of pretzels produced per day, whereas Detroit's distribution is normal. The company measures the number of pretzels produced per day for 40 days in Minneapolis and 25 days in Detroit. Can the company assume that the shape of the sampling distribution of the difference in means between the two factories is normal? Why or why not?
Yes; Minneapolis factory has n >= 30 and Detroit factory has a normal population distribution.