Answer in Statistics and Probability for xy-xy #248976

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. = _____, = _____.

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

Step 4: Decision rule. ____________________________________________________________

Step 5. Conclusion. ______________________________________________________________

Solution:

“bar{x}=70 \nnn=50 \nnmu=72 \nnsigma = 12”

Step 1: State the hypotheses.

“Ho: mu = 72 \nnHa: mu<72”

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

the level of significance = 0.01,

“Z_{cr} = -2.32.”

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

“Z = frac{bar{x} – mu}{sigma / sqrt{n}} \nnZ = frac{70-72}{12 / sqrt{50}} = -1.178”

= -1.178.

Step 4: Decision rule. Reject Ho if “Z u2264 – 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.