Question

set	Hypothesis	u^	μ0	o^	n	α
a)	μ ≠ μ0	14.2	10	4	29	0.05
b)	μ > μ0	98.3	99.3	6.8	21	0.10
c)	μ < μ0	19.1	20	9.1	23	0.01

a)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value = ________ ; test statistic = __________
Decision:--Select---Reject H0 or Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d = ______ ; Magnitude:--Select---na, trivial effect, small effect, medium effect, large effect
r² = ____; Magnitude: -Select---na, trivial effect, small effect, medium effect, large effect

b)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value = ____ ; test statistic = _______
Decision:-Select---Reject H0 or Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d = _____; Magnitude: --Select---na, trivial effect, small effect, medium effect, large effect
r² = ____; Magnitude:--Select---na, trivial effect, small effect, medium effect, large effect

c)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value = ______ ; test statistic = ____
Decision: --Select---Reject H0 or Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d =______ ; Magnitude: --Select---na, trivial effect, small effect, medium effect, large effect
r² = ______; Magnitude: Select---na, trivial effect, small effect, medium effect, large effect

Answer 1

a) To test:

     Vs at 5% level of significance

As mentioned in the problem, since, the population standard deviation is unknown, the appropriate test to test the above hypothesis would be a one sample t test:  

The test statistic is given by:

with critical region for two tailed test given by

For alpha = 0.05, and for n - 1 = 290 - 1 = 289 degrees of freedom, (since, the degrees of freedom is large, we may go for the excel function instead of the t table):

we get t0.05,289 = 1.968

Substituting the values,

= 17.88

t = 17.88

Since, t = 17.88 > 1.968 lie in the rejection / critical region, we may reject H0 at 5% level.

Computing the effect size:

Cohen's d:

- Large Effect ( )

And r2 can be computed using the formula:

- Large effect ()

b) To test:

     Vs at 10% level of significance

As mentioned in the problem, since, the population standard deviation is unknown, the appropriate test to test the above hypothesis would be a one sample t test:  

The test statistic is given by:

with critical region for right tailed test given by

For alpha = 0.10, and for n - 1 = 210 - 1 = 209 degrees of freedom, (since, the degrees of freedom is large, we may go for the excel function instead of the t table):

we get t0.10,209 = 1.286

Substituting the values,

= -2.131

t = -2.131

Since, t = -2.131<1.286 does not lie in the rejection / critical region, we fail to reject H0 at 10% level.

Computing the effect size:

Cohen's d:

- Trivial Effect

And r2 can be computed using the formula:

  

- Small effect

c) To test:

     Vs at 5% level of significance

As mentioned in the problem, since, the population standard deviation is unknown, the appropriate test to test the above hypothesis would be a one sample t test:  

The test statistic is given by:

with critical region for left tailed test given by

For alpha = 0.01, and for n - 1 = 230 - 1 = 229 degrees of freedom, (since, the degrees of freedom is large, we may go for the excel function instead of the t table):

we get t0.01,229 = -2.343

Substituting the values,

= -1.5

t = -1.5

Since, t = -1.5 > -2.343 does not lie in the rejection / critical region, we fail to reject H0 at 1% level.

Computing the effect size:

Cohen's d:

- Trivial Effect

And r2 can be computed using the formula:

- Trivial effect