Question

A sample of n = 4 is selected from a population with µ = 50. After a treatment is administered to the individuals in the sample, the mean is found to be M = 55 and the variance is s2= 64.

a. For a two-tailed test, what is the null hypothesis using statistical notation?

b. For a two-tailed test, what is the alternative hypothesis using statistical notation?

c. What is the estimated standard error?

d. What is the value/s for tcrit for a two-tailed test with α = .05

e. What is the value/s for tobt?

f. Is the data statistically significant for a two-tailed test with α = .05? NOTE: simply writing that the effect is significant (e.g., only writing “reject the null”) without showing any work/calculations in parts a-e will result in point zero points.

g. What is estimated Cohen’s d?

h. if you increased the size of the sample, how will this affect the likelihood of rejecting the null hypothesis?

i. If the variance increases, how will this affect the likelihood of rejecting the null hypothesis?

Answer 1

A sample of n = 4 is selected from a population with µ = 50. After a treatment is administered to the individuals in the sample, the mean is found to be = 55 and the variance is s2= 64.

Since the sample size is small we are goingto assume that the data comes from a normal population.

a. For a two-tailed test, what is the null hypothesis using statistical notation?

This is what we previously know so we want to test this one.

b. For a two-tailed test, what is the alternative hypothesis using statistical notation?

Since it is two tailed we test for equality

c. What is the estimated standard error?

Std error =

Std error = 4

d. What is the value/s for tcrit for a two-tailed test with α = .05

since it is two tailed so p = 0.05 /2

C.V. =

=

C.V. = 3.1824   .......using t-dist tables p = 0.025 and df =3

e. What is the value/s for tobt?

Test Stat =

Test stat = 1.25

f. Is the data statistically significant for a two-tailed test with α = .05? NOTE: simply writing that the effect is significant (e.g., only writing “reject the null”) without showing any work/calculations in parts a-e will result in point zero points.

Since Test Stat < C.V.

The result is not significant. We do not reject the null hypothesis

Conclusion: The population mean is significantly 50 for the treatment.

g. What is estimated Cohen’s d?

Cohen's d =

Cohen's d =0.625 ............S = sq root of 64

It is medium

h. if you increased the size of the sample, how will this affect the likelihood of rejecting the null hypothesis?

Increasing the sample size will increase the likelihood of rejecting the null hypothesis.

Test Stat = =

So numerator will increase with 'n'.Therfore T.S. will increase. So it will have more chances to be greater than C.V.

i. If the variance increases, how will this affect the likelihood of rejecting the null hypothesis?

Increase in variance will lead to decrease in likelihood of rejecting the null hypothesis.

Test Stat =

So denomianator will increase with 'S'.Therfore T.S. will decrease. So it will have less chances to be greater than C.V.