Hypothesis Testing Flashcards
The null hypothesis (H0)(H0) is
a statement about a topic of interest about the population. It is typically based on historical information or conventional wisdom. We always start a hypothesis test by assuming that the null hypothesis is true and then test to see if we can nullify it using evidence from a sample. The null hypothesis is the opposite of the hypothesis we are trying to prove (the alternative hypothesis).
The alternative hypothesis (Ha)
is the theory or claim we are trying to substantiate.
2 steps before conducting hypothesis test:
1) Determine whether to analyze a change in a single population or compare two populations.
2) Determine whether to perform a one-sided or two-sided hypothesis test.
To conduct a hypothesis test, we must follow these steps:
1) State the null and alternative hypotheses.
2) Choose the level of significance for the test.
3) Gather data about a sample or samples.
4) To determine whether the sample is highly unlikely under the assumption that the null hypothesis is true, construct the range of likely sample means or calculate the p-value.
The p-value is
the evidence against the null hypothesis. the smaller it is, the stronger the evidence. the likelihood of obtaining a sample as extreme as the one we’ve obtained, if the null hypothesis is true.
What does p-value of a one-sided test equal?
half the p-value of a two-sided hypothesis test.
When do we not have sufficient evidence to reject the null hypothesis?
If the sample mean falls in the range of likely sample means, or if its p-value is greater than the stated significance level,
When do we have sufficient evidence to reject the null hypothesis?
If the sample mean falls in the rejection region, or if it has a p-value lower than the stated significance level
When can we accept the null hypothesis?
Never. We either reject them or fail to reject them
What are 2 errors that can occur?
A type I error is often called a false positive (we incorrectly reject the null hypothesis when it is actually true)
type II error is often called a false negative (we incorrectly fail to reject the null hypothesis when it is actually not true)
EXCEL formula for calculating the range of likely sample means
CONFIDENCE.NORM or CONFIDENCE.T
=T.TEST(array1, array2, tails, type)
A manager of a factory wants to know if a new quality check protocol has decreased the number of units a worker produces in a day. Before the new protocol, a worker could produce 27 units per day. What alternative hypothesis should the manager use to test this claim?
µ < 27 units
The manager wants to know if the new quality check protocol has decreased the average number of units a worker can produce per day. For a one-sided test, the manager should use the alternative hypothesis Ha: μ<27 units. This is the claim the manger wishes to substantiate.
A manager of a factory wants to know if a new quality check protocol has decreased the number of units a worker produces in a day. Before the new protocol, a worker could produce 27 units per day. What null hypothesis should the manager use to test this claim?
µ ≥ 27 units
This is the null hypothesis. Remember that the null and alternative hypotheses are opposites.
If you are performing a hypothesis test based on a 90% confidence level, what are your chances of making a type II error?
It is not possible to tell without more information. The confidence level does not provide any information about the likelihood of making a type II error. Calculating the chances of making a type II error is quite complex and beyond the scope of this course.
If you are performing a hypothesis test based on a 90% confidence level, what are your chances of making a type I error?
10%
The probability of a type I error is equal to the significance level, which is 1–confidence level. A 90% confidence level indicates that the significance level is 10%. Therefore there is a 10% chance of making a type I error.
