For each of the following test, outline a research scenario and use any hypothetical data to show how the test is conducted. Paired two-sample t-test

mattgondek4 2020-10-21 Answered
For each of the following test, outline a research scenario and use any hypothetical data to show how the test is conducted.
Paired two-sample t-test
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

hajavaF
Answered 2020-10-22 Author has 90 answers

Correlated samples t test or paired t test or repeated measures t test:
The paired t is used when the two sample are paired or related samples. When the sample is measured twice, or paired samples are taken, then the two samples would be dependent. This indicates that paired t test is used for comparing the dependent samples.
Conditions to perform the paired t-test:
Dependent variable is measured on a continuous scale.
Each score in one sample is paired with a particular score in the other sample.
The difference of the either group follows normal distribution.
Example:
Junior school research team would like to examine whether students performance in math is increased after recruiting two high qualified math teachers. Both pre-test and post-test scores of a random sample of 20 students were recorded. The mean difference between post-test and pre-test score was 15.4 with standard deviation 3.4. Does the data provide evidence to conclude that students performance in math is increased. Use 5% level of significance.
Hypotheses and level of significance:
The hypotheses to be tested are:
Null hypothesis:
H0:μd=0
Alternative hypothesis:
H1:μd>0
Assume the level of significance is given as α=0.05.
Paired t-test statistic:
In order to test a hypothesis regarding whether the difference between a paired set of observations (xi,yi) is significant or not, the paired t-test is used.
The test statistic for the paired t-test is given as follows:
t=dse(d) where,
d=1nmi=1n(xiyi)
se(d)=
standard error of d
=standard error of dn
=1n1mi=1n(did)2n
The following table shows the necessary calculations for finding the test statistic:
sed=1n1mi=1n(did)2n
=3.420
0.7603
=20.2552
df=n1
=201
=19
Thus, t=20.2552.
Decision rule:
If the p-value is less than the level of significance then reject the null hypothesis. Otherwise fail to reject the null hypothesis
The p-value is given by:
The p-value =0(From excel=T.DIST.RT(20.2552,19))
Since the p-value (=0)
less than level of significance (=0.05), decision is to reject the null hypothesis.
There is sufficient evidence to conclude that student’s performance in math is increased.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2020-11-01
Solve the following problems applying Polya’s Four-Step Problem-Solving strategy.
If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?
asked 2021-03-02
In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference
asked 2021-10-11
What is an advantage of using a stem-and-leaf plot instead of a histogram? What is a disadvantage?
asked 2021-10-17
Describe the basic characteristics that define an independent-measures, or a between-subjects, research study.
asked 2021-10-25
For the following experiment, state the type of test we should use. Assume homogeneity of variance (where applicable), unless something is directly stated (e.g., "the data are not at all normal") or otherwise indicated (viz., by the inspection of the data) which would indicate an obvious violation of an assumption. This means you must inspect the data for violations of all assumptions. Assume n is large enough, unless stated. Assume σ is unknown, unless stated.
Brianna works at an infant/toddler center and wants to know whether children at the age of two have a preference for a certain type of toy. She puts four different toys in front of the infant/toddler and sees which toy the child crawls to first.
1) a one-sample t-test for means
2) none of the other tests
3) an independent samples t-test with heterogeneity of variance
4) a related samples t-test
5) and independent samples t-test with homogeneity of variance
6) a chi-squared goodness-of-fit test
7) a z-test for the difference between proportions
8) a one sample z-test for proportions
9) a one-sample z test for means
asked 2020-11-09
Consider a group of 8 people. Among them, there is one pair of twins. These 8 people are taken into two different rooms, Room A and Room B, with four people to each room. If all groups of four people are equally likely, find the probability that the twins will be sent into the same room.
asked 2021-10-14
How can the normal distribution be used to test hypotheses about populations? Also, how might you surmise that you can use this logic to test a hypothesis such as caffeine improves memory in the caffeine study.