Question

The cost of a daily newspaper varies from city to city. However, the variation among prices
remains steady with a standard deviation of 6¢. A study was done to test the claim that the
average cost of a daily newspaper is 35¢. Twelve costs yield an average cost of 30¢ with a standard
deviation of 4¢. Do the data support the claim at the 1% level?

Answer 1

Firstly we determine null and alternative hypotheses. Since the test is two-tailed we got such:

$$H_0: \mu = 35$$ $$H_1: \mu \neq 35$$

The next step of testing the claim is calculating test statistics. We use the formula:

$$z = \frac{\bar{x} - \mu_0}{\sigma_0 / \sqrt{n}}$$

Test statistics:

$$z = \frac{30 - 35}{6 / \sqrt{12}} = -2.88$$

Critical values of the two-tailed test is determined using the formula:

$$\frac{z \alpha_1}{2} z_{1 - \frac{\alpha}{2}}$$

In our case $\alpha = 0.01$ and thus

$$z_{\text{critical}} = z_{\frac{0.01}{2}} = -2.57$$

Since $|z| > |z_{\text{critical}}|$ there is no enough evidence to conclude that $\mu \neq 35$.