Question

A psychiatrist is testing a new antianxiety drug, which seems to have the potentially harmful side effect of lowering the heart rate. For a sample of 50 medical students whose pulse was measured after 6 weeks of taking the drug, the mean heart rate was 70 beats per minute (bpm). If the mean heart rate for the population is 72 bpm with a standard deviation of 12, can the psychiatrist conclude that the new drug lowers heart rate significantly? (Set the level of significance to 0.01.)

Solution: Step 1: State the hypotheses.

Ho: _______________________________________________________________

Ha: _______________________________________________________________

Step 2: The level of significance and the critical region. 𝛼 = _____, 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 = _____.

Step 3: Compute for the value of one sample test. 𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑑 𝑡𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 = _______.

Step 4: Decision rule. ____________________________________________________________

Step 5. Conclusion. ______________________________________________________________

Answer 1

Solution:

$\bar{x}=70 \\ n=50 \\ \mu=72 \\ \sigma = 12$

Step 1: State the hypotheses.

$Ho: \mu = 72 \\ Ha: \mu<72$

Step 2: The level of significance and the critical region. 𝛼

the level of significance = 0.01,

𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 $Z_{cr} = -2.32.$

Step 3: Compute for the value of one sample test.

$Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \\ Z = \frac{70-72}{12 / \sqrt{50}} = -1.178$

𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑑 𝑡𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 = -1.178.

Step 4: Decision rule. Reject Ho if $Z ≤ - Z_{cr}.$

Step 5. Conclusion.

$Z=-1.178 > Z_{cr} = -2.32$

Accept Ho. We can conclude, that the new drug does NOT lower heart rate significantly.