Normal Distribution and CLT
Draw a normal distribution, with the empirical rule labeled
Would Include the imagine but it makes me pay
What is a type one error?
The decision is to reject H0 when H0 is true
What is the confidence interval tell us?
It provides a range of reasonable values in which we expect the population parameter to fall.
What makes an equation an exponential function? Write an example on the board with the answer
By definition, an exponential function has a constant as a base and an independent variable as an exponent.
What number represents the normal distribution as a whole if it were a probability?
1
What is a type two error?
The decision is not to reject H0 when, in fact, H0 is false
What is the alpha? How do you find it?
α is the probability that the interval does not contain the unknown population parameter. Subtract 1- the CL
What must an exponential function have variable wise to call it a exponential function?
It must have an "a" and a "b" varible that do not equal zero.
Explain the Central Limit Theorem
if we collect samples of size n with a "large enough n," calculate each sample's mean, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape.
Suppose the null hypothesis, H0, is: a patient is not sick. Which type of error has the greater consequence, Type I or Type II?
Type 2, you think the patient is not sick yet they are, but you turn them away
The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. What is the confidence interval?
CI: (24.52,36.28)
Draw a graph for a exponential function
It won't let me put images so please do it.
What are the two rules that must be passed for a normal distribution to be assumed?
2. The normal distribution is stated in the question
Suppose the null hypothesis, H0, is: The victim of an automobile accident is alive when they arrive at the emergency room of a hospital. What error has the greater consequence?
Type I error: The emergency crew thinks that the victim is dead when, in fact, the victim is alive.
If it were later determined that it was important to be more than 90% confident and a new survey were commissioned, how would it affect the minimum number you need to survey? Why?
To maintain the same error bound, the size of the sample needs to increase.
If we invest $3,000 in an investment account paying 3% interest compounded quarterly, how much will the account be
worth in 10 years?
Because we are starting with $3,000, Our interest rate is 3%, so Because we are compounding
quarterly, we are compounding 4 times per year, so
The account will be worth about $4,045.05 in 10 years
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. What is the z-score for a patient who takes ten days to recover? Interpret this
The z-score is 2.2, the patient takes much longer to recover than the average patient in the hospital.
How do we statistically prove if the null hypothesis is correct or incorrect?
We must find our t-statistic and use that to find the p-value.
If the p is low REJECT THE HO
What is meant by the term “90% confident” when constructing a confidence interval for a mean?
If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.
Rewrite 4 to the power of 3= 64 in log
log4(64)=3