AP Statistics : Estimation
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Example Questions
Example Question #1 : How To Estimate Population Parameters
What is 
Example Question #1 : How To Estimate Population Parameters
Example Question #1 : Estimation
The next local election is predicted to have a 
If you remember the required formula, this problem is rather simple. Plug in the given numbers and simplify:
If you don't remember the formula, this problem is more challenging. Your best bet in this case is to construct the confidence interval and rearrange to solve for the required sample size.
Example Question #1 : How To Estimate Margins Of Errors
When dealing with confidence intervals, the margin of error gets smaller when z* gets ________ and n gets _________.
smaller . . . smaller
larger . . . larger
larger . . . smaller
There is no way to affect the margin of error in confidence intervals
smaller . . . larger
smaller . . . larger
For confidence intervals, a small margin of error is preferred, as it indicates that the parameter of interest has been narrowed down to a precise interval. Having a large sample population to work from as well as a small z* (z* gets smaller as the confidence level percent gets lower) can help obtain a small margin of error.
Example Question #1 : Estimation
Example Question #1 : How To Find Point Estimators
Example Question #1 : Confidence Intervals
Suppose you have a normally distributed variable with known variance. How many standard errors do you need to add and subtract from the sample mean so that you obtain 95% confidence intervals?
To obtain 95% confidence intervals for a normal distribution with known variance, you take the mean and add/subtract 
Example Question #2 : Confidence Intervals
An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000. The standard deviation of the 24-car sample is $2,500.
Provide a 98% confidence interval for the true mean cost of repair.
Standard deviation for the samle mean:
Since n < 30, we must use the t-table (not the z-table).
The 98% t-value for n=24 is 2.5.
Example Question #1 : Confidence Intervals
300 hundred eggs were randomly chosen from a gravid female salmon and individually weighed. The mean weight was 0.978 g with a standard deviation of 0.042. Find the 95% confidence interval for the mean weight of the salmon eggs (because it is a large n, use the standard normal distribution).
Because we have such a large sample size, we are using the standard normal or z-distribution to calculate the confidence interval.
Formula:
We must find the appropriate z-value based on the given 
Then, find the associated z-score using the z-table for
Now we fill in the formula with our values from the problem to find the 95% CI.
Example Question #1 : Confidence Intervals
A sample of 
Find the 
Because we are only given the sample standard deviation we will use the t-distribution to calculate the confidence interval.
Appropriate Formula:
Now we must identify our variables:
We must find the appropriate t-value based on the given
t-value at 90% confidence:
Look up t-value for 0.05, 55 , so t-value= ~ 1.6735
90% CI becomes:
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