Questions: Your medical research team is investigating the mean cost of a 30-day supply of a certain heart medication. A pharmaceutical company thinks that the mean cost is more than 97. You want to support this claim. How would you write the null and alternative hypotheses? H₀ ◀ H₁ ◀

Solution Steps

We set up the null and alternative hypotheses as follows:

• Null Hypothesis \( H_0 \): The mean cost is \( \mu \leq 97 \).
• Alternative Hypothesis \( H_1 \): The mean cost is \( \mu > 97 \).

The standard error \( SE \) is calculated using the formula:

\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{30}} \approx 1.8257 \]

The test statistic \( Z_{test} \) is calculated using the formula:

\[ Z_{test} = \frac{\bar{x} - \mu_0}{SE} = \frac{100 - 97}{1.8257} \approx 1.6432 \]

For a right-tailed test, the p-value is calculated as:

\[ P = 1 - T(z) \approx 0.0502 \]

To determine whether to reject the null hypothesis, we compare the p-value to the significance level \( \alpha = 0.05 \):

• Since \( P \approx 0.0502 > 0.05 \), we fail to reject the null hypothesis.

Final Answer