Question

Given a sample size of 65, with sample mean 726.2 and sample standard deviation 85.3,
we perform the following hypothesis test.
0 H :  750
1 H :  750
What is the conclusion of the test at the   0.10 level? Explain your answer.

Answer 1

Conditions

Given a sample size of 65, with sample mean 726.2 and sample standard deviation 85.3, we perform the following hypothesis test.

$$0 \mathrm{H}: \mathrm{m} = 750$$ $$1 \mathrm{H}: \mathrm{m} < 750$$

What is the conclusion of the test at the $a = 0.10$ level? Explain your answer.

Solution

This is the question for one-sampled t-criterion.

$$H_0: M_1 = 750$$ $$H_a: M_1 < 750$$ $$t = \frac{|x - m|}{s_X / \sqrt{n}}$$ $$s_X^2 = \sum_{t=1}^{n} (X_t - \bar{X})^2 / (n - 1)$$

For this example:

$$t = 2.249493$$

The degrees of freedom:

$$k = 65 - 1 = 64$$

For these degrees of freedom the t-criteria value is:

$$1.997 - \text{for } p = 0.95$$ $$t = 2.249493 > 1.997$$

We can make a conclusion, that with probability $95\%$ H0 is rejected, Ha – approved.