Question

We would like to conduct a hypothesis test to determine whether the true mean pulse rate of healthy adults differs from 75 beats per minute. Pulse rates of healthy adults are known to follow a normal distribution with standard deviation 10 beats per minutes. We will record the pulse rates of a random sample of 15 healthy adults. It is decided that that null hypothesis will be rejected if X≤ 70.146 or X ≥ 79.854. What is the approximate significance level of the test?

a. 0.02
b. 0.03
c. 0.04
d. 0.05
e. 0.06

Answer 1

Answer on Question #84611 – Math – Statistics and Probability

Question

We would like to conduct a hypothesis test to determine whether the true mean pulse rate of healthy adults differs from 75 beats per minute. Pulse rates of healthy adults are known to follow a normal distribution with standard deviation 10 beats per minutes. We will record the pulse rates of a random sample of 15 healthy adults. It is decided that that null hypothesis will be rejected if $X \leq 70.146$ or $X \geq 79.854$. What is the approximate significance level of the test?

a. 0.02

b. 0.03

c. 0.04

d. 0.05

e. 0.06

Solution

$$\alpha\% CI = \left(\bar{x} - z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}}, \bar{x} + z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}}\right) = (70.146, 79.854).$$ $$\text{So, } 2z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}} = 79.854 - 70.146 = 9.708 \rightarrow z_{\frac{\alpha}{2}} = \frac{9.708 * \sqrt{15}}{2 * 10} = 1.880.$$

Thus, the significance level, $\alpha = 0.0601$. The approximate significance level of the test is e) 0.06.

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