Distributions
Represents the spread of the distribution
Standard Deviation
Also known as alpha risk
Level of significance
This claim is assumed to be true in a hypothesis test
Null hypothesis
Suppose ‘Buffalonians’ drive an average of 12,000 miles per year with a standard deviation of 2,580 miles per year. What is the probability that a randomly selected driver will drive more than 12,500 miles?
0.4232
The center of the distribution
The mean
Increasing this will increase the width of a confidence interval for a population mean
Level of confidence
When you fail to reject a false null hypothesis
Type II error
Suppose ‘Buffalonians’ drive an average of 12,000 miles per year with a standard deviation of 2,580 miles per year. What is the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles?
0.1225
Causes the curve to becomes tall and narrow
The decrease in the standard deviation of a normal distribution
For a confidence level of 98%, find the Z-critical value. (Report answer to 3 decimal places)
2.326
The probability of observing the experiment result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true
P-value
Suppose American Express reports that credit card balances are normally distributed, with a mean of $2800 & a standard deviation of $500. What is the probability that a randomly selected credit card holder has a credit card balance less than $2500?
0.2743
Causes the curve to shift to the right
Increase in the mean of a normal distribution
A random sample of 30 UB students finds an average commute time of 20 minutes with a sample standard deviation of 10 minutes. Assuming commute time follows a normal distribution construct a 95% confidence interval for the average commute time for all UB North students. (Report answer to 2 decimal places)
LL: 16.27, UL: 23.73
H0:μ=53.5
H1:μ≠53.5
Your sample consists of 47 subjects, with a mean of 54 and a sample standard deviation (s) of 4.2.
Calculate the test statistic. (Report answer to 2 decimal places)
t = 0.82
Suppose American Express reports that credit card balances are normally distributed, with a mean of $2800 & a standard deviation of $500. You randomly select 25 credit card holders. What is the probability that their mean credit card balance is less than $2500?
0.0013
Indicates by how many standard deviations a score is above or below the mean
Z-Scores
The number of standard errors (or standard deviations) to move from the mean of a sampling distribution to correspond to a specified level of confidence.
Critical Value
You wish to test the following claim (Ha) at a significance level of α=0.005α
Ha:μ≠66.6
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=9 with mean x̅=82.9 and a standard deviation of s=12.9
What is the p-value for this sample? (Report answer accurate to four decimal places)
P-value = 0.0053
Suppose American Express reports that credit card balances are normally distributed, with a mean of $2800 & a standard deviation of $500. You randomly select 5 credit card holders. What is the probability that their mean credit card balance is between $2000 and $2500?
0.0897