Statistics Chapter 9 Test
What do we mean when we say a test is significant? Does this necessarily mean the results are important?
A significant test means we reject the null hypothesis. This does not necessarily imply that the results are practically significant.
What is a null hypothesis H0?
A working hypothesis making a claim about the population parameter in question.
What is an alternate hypothesis H1?
Any hypothesis that differs from the original claim being made.
If we fail to reject (i.e., "accept") the null hypothesis, does this mean that we have proved it to be true beyond all doubt? Explain your answer.
No, it suggests that the evidence is not sufficient to merit rejecting the null hypothesis.
What is the level of significance of a test?
The probability of a type I error.
To use the normal distribution to test a proportion p, the conditions np > 5 and nq > 5 must be satisfied. Does the value of p come from H0, or is it estimated by using p̂ from the sample?
The value of (p---rho) comes from H0.
What is a type I error?
Type I Error is rejecting the null hypothesis when it is true.
What is a type II error?
Type II Error is failing to reject the null hypothesis when it is false.
Consider a test for μ. If the P-value is such that you can reject H0 for α = .01, can you always reject H0 for α = .05? Explain your answer.
Yes. If H0 is rejected at the 1% level it will always be rejected at the 5% level.
What is the probability of a type II error?
beta
When using the Student's t distribution to test μ, what value do you use for the degrees of freedom?
n-1
Consider a test for μ. If the P-value is such that you can reject H0 at the 5% level of significance, can you always reject H0 at the 1% level of significance? Explain your answer.
No. If the P-value lies between 0.01 and 0.05 you would reject the 5% level of significance, but not at the 1% level.
In a statistical test, we have a choice of a left-tailed test, a right-tailed test, or a two-tailed test. Is it the null hypothesis or the alternate hypothesis that determines which type of test is used? Explain your answer.
The alternative hypothesis because it specifies the region of interest for the parameter in question.
To test μ for an x distribution that is mound-shaped using sample size n ≥ 30, how do you decide whether to use the normal or Student's t distribution?
If the (sigma) is known, use the standard normal distribution. If (sigma) is unknown, use the Student's "t" distribution with n-1 degrees of freedom.
If we reject the null hypothesis, does this mean that we have proved it to be false beyond all doubt? Explain your answer.
No, the test was conducted with a risk of a type I error.