Definitions
What are the two conditions for a t-test?
This test is applied to:
- The same population
- The data must be normally distributed
A ________ is a parametric hypothesis test used to compare one or two group means (μ) when the population standard deviation (σ) is unknown.
t-test
A ___________ compares data taken from two different populations
Two-sample t-test
A ___________ compares a sample mean in two different moments
One-sample t-test
A manufacturer claims its LED light bulbs last an average of 1,000 hours. A quality control inspector randomly selects 15 bulbs and records the following lifespans (hours): 978, 1010, 965, 982, 1024, 990, 1003, 971, 1018, 985, 962, 995, 1007, 973, 1012.
Establish the null and alternative hypotheses.
State hypotheses:
H₀: μ = 1,000 hours | H₁: μ ≠ 1,000 hours (two-tailed — testing whether the true mean differs from the claim in either direction)
Solve part b of problem 1 (8G, page 409)
b. One-tailed test
You want to check whether a new drug increases memory performance. You test the memory performance of 40 people before and after they take the medicine.
¿What type of test should you apply?
a. Two-tailed t-test
b. One-tailed t-test
b. One-tailed t-test
You want to check whether a new drug increases memory performance. You test the memory performance of 40 people before and after they take the medicine.
¿What type of test should you apply?
a. One-sample t-test
b. Two-sample t-test
a. One-sample t-test
Solve part a of problem 1 (8G, page 409)
a.
H0: μ weight of apples from trees in shade = μ weight of apples from trees not in shade
H1: μ weight of apples from trees in shade < μ weight of apples from trees not in shade
You want to check whether a new drug increases memory performance. You test the memory performance of 40 people before and after they take the medicine.
Establish the null and alternative hypotheses.
H0: There is no difference between the memory performance of the 40 people before they take the medicine and the memory performance after they take the medicine
μ before the medicine = μ after the medicine
H1: μ memory after the medicine > μ memory before the medicine
A screw factory complains about very high downtime at its 5 production plants. You are now to find out whether a newly introduced lubricant has an influence on the downtime. For this, you compare the downtime of the 5 plants before and after the introduction of the new lubricant.
Establish the null and alternative hypotheses
H0: There is no difference between the downtime before applying the new lubricant and the downtime after applying the new lubricant
μ before the lubricant = μ before the lubricant
H1: μ before the lubricant > μ after the lubricant
If the p-value in a test is p= 0.0573, find the conclusion of the test:
a) at a 10% significance level
b) at a 5% significance level
a) At a 10% significance level
H0 is rejected because 0.0573 < 0.10
b) At a 10% significance level
H0 is accepted because 0.0573 > 0.05
Create your own example of a two-tailed t-test
Any correct example of a two-tailed t-test
Create your own example of a two-sample t-test
Any correct example of a two-sample t-test
Solve parts c and d of problem 1 (8G, page 409)
c. t=-0.687, p=0.251, df=16 at the 10% significance level
d. Due to 0.251 > 0.10, the H0 is accepted