A Hypothesis Is a Claim
A hypothesis is a claim
Population mean
The mean monthly cell phone bill in this city is μ = $42
Population proportion
Example: The proportion of adults in this city with cell phones is π = 0.68
States the claim or assertion to be tested Is always about a population parameter, not about a sample statistic
Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 )
Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove
Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 )
Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove
Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 )
Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove
If the sample mean is close to the stated population mean, the null hypothesis is not rejected.
If the sample mean is far from the stated population mean, the null hypothesis is rejected.
How far is “far enough” to reject H0?
The critical value of a test statistic creates a “line in the sand” for decision making -- it answers the question of how far is far enough.
Type I Error
Reject a true null hypothesis
Considered a serious type of error
The probability of a Type I Error is
Called level of significance of the test
Set by researcher in advance
Type II Error
Failure to reject a false null hypothesis
The probability of a Type II Error is β
Type I and Type II errors cannot happen at the same time A Type I error can only occur if H0 is true A Type II error can
Population mean
The mean monthly cell phone bill in this city is μ = $42
Population proportion
Example: The proportion of adults in this city with cell phones is π = 0.68
States the claim or assertion to be tested Is always about a population parameter, not about a sample statistic
Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 )
Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove
Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 )
Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove
Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 )
Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove
If the sample mean is close to the stated population mean, the null hypothesis is not rejected.
If the sample mean is far from the stated population mean, the null hypothesis is rejected.
How far is “far enough” to reject H0?
The critical value of a test statistic creates a “line in the sand” for decision making -- it answers the question of how far is far enough.
Type I Error
Reject a true null hypothesis
Considered a serious type of error
The probability of a Type I Error is
Called level of significance of the test
Set by researcher in advance
Type II Error
Failure to reject a false null hypothesis
The probability of a Type II Error is β
Type I and Type II errors cannot happen at the same time A Type I error can only occur if H0 is true A Type II error can