Mean CLT Practice
X bar is...
The sample mean
P hat is...
The sample proportion
T/F: We use X bar or P hat to estimate intervals because we do not know the data for a population
TRUE
We describe the confidence interval as...
point estimate +/- margin of error
How do we determine the margin of error?
p hat or x bar +/- z(a/2)(standard deviation)
If the data is not strongly skewed and n>=30, then...
The CLT can be applied! X bar is approximately normal with mean of mu and sd of sigma/sqrt(n)!
The CLT can be applied! P hat is approximately normal with mean of p and sd of sqrt(p[1-p]/n)
The point estimate for population proportion is...
The point estimate for the population mean is...
p hat = x/n
x bar
How do we phrase our answer when using a 95% confidence interval
"We are 95% confident..."
What if we cannot use the Empirical Rule when calculating margin of error?
Then z(a/2) will be given to you!
In 2021, it was found that the average life span of tigers has increased from 10 years to 15 years, and was found to be approximately normal. The standard deviation is 2.5 years. Researchers took a sample of 5 tigers to observe. Can the CLT be used?
Yes, because the distribution is said to be approximately normal.
A 2023 study on the aerodynamics of cows versus cars was conducted and it was concluded that 27% of cows are more aerodynamic than cars. If 455 cows are studied, can the CLT be applied?
Yes, because np(1-p) is greater than 10.
According to the National Health Statistics Reports, a sample of 360 one-year-old baby boys in the US had a mean weight of 25.5 pounds. What is the point estimate for the mean weight of all one-year-old baby boys in the US?
x bar = 25.5
T/F: When we say that we are "95% confident" in our interval estimate, we are saying that there is a 95% probability that the population parameter is contained in that one specific interval.
FALSE
The width of a confidence interval is...
In 2021, it was found that the average life span of tigers has increased from 10 years to 15 years, and was found to be approximately normal. The standard deviation is 2.5 years. Researchers took a sample of 5 tigers to observe. Describe the distribution.
Mean:
Sd:
A 2023 study on the aerodynamics of cows versus cars was conducted and it was concluded that 27% of cows are more aerodynamic than cars. If 455 cows are studied, how do we describe the distribution?
Mean: 0.27
SD: 0.021
The drug Eliquis is used to help prevent blood clots in certain patients. In clinical trials, among 5924 patients treated with Eliquis, 153 developed nausea. What is the point estimate for the proportion of those who develop nausea in all patients treated with Eliquis?
0.026
If we denote the level of confidence as (1-a)(100%), what would a 95% confidence level be denoted as?
(1-0.05)(100%)
Fun question: What is the oldest known fruit?
Fig
okay i lowkey didn't complete this question so that's why it didn't show up :(
:)
A 2023 study on the aerodynamics of cows versus cars was conducted and it was concluded that 27% of cows are more aerodynamic than cars. If 455 cows are studied, what is the probability that more that 79% are aerodynamic? Is this unlikely?
0, yes, it is unlikely
0.33; No, but it should be close
The drug Eliquis is used to help prevent blood clots in certain patients. In clinical trials, among 5924 patients treated with Eliquis, 153 developed nausea. Using the Empirical Rule, a 95% confidence interval for the proportion of all patients that develop nausea is...
We are 95% confident that the proportion of all Eliquis users that experience nausea is between 0.022 and 0.03
According to the National Health Statistics Reports, a sample of 360 one-year-old baby boys in the US had a mean weight of 25.5 pounds. If it is known that the standard deviation of the weight of one-year-old boys is 1.5 lbs, describe the sampling distribution and find the margin of error using a 95% confidence interval.
X bar is approximately normal with mean 25.5, sd of 0.079
+/- 0.158