Question

2. If a sample of n = 49 was obtained a

= 260, S = 6. Try the following hypothesis: Use a = 0.10

* Is there evidence that the average mx is greater than 247?
* Estimate a confidence interval of 90% for the true value of the average of this population.
* Determine β and the power of the test. (1-β) of the previous hypothesis
* Determine the p-value for the previous test.

Answer 1

Answer:

MINITAB used

2. If a sample of n = 49 was obtained a

= 260, S = 6. Try the following hypothesis: Use a = 0.10

One-Sample T

(z-1)

Descriptive Statistics

N	Mean	StDev	SE Mean	90% Lower Bound for μ
49	260.000	6.000	0.857	258.886

μ: mean of Sample

Test

Null hypothesis	H₀: μ = 247
Alternative hypothesis	H₁: μ > 247

T-Value	P-Value
15.17	0.000

* Is there evidence that the average mx is greater than 247?

Calculated t=15.17,

Critical t with 0.10 level at 48 Df =1.30, calculated t value 15.17 > critical t value, Ho is rejected.

There is enough evidence that the average mx is greater than 247.

* Estimate a confidence interval of 90% for the true value of the average of this population.

Descriptive Statistics

N	Mean	StDev	SE Mean	90% CI for μ
49	260.000	6.000	0.857	(258.562, 261.438)

μ: mean of Sample

* Determine β and the power of the test. (1-β) of the previous hypothesis

Power and Sample Size

1-Sample t Test

Testing mean = null (versus > null)

Calculating power for mean = null + difference

α = 0.1 Assumed standard deviation = 6

Results

Difference	Sample Size	Power
13	49	1

power of the test (1-β) = 1.0

β = 0.00

* Determine the p-value for the previous test.

P=0.000