Solve the Problem $\alpha = 0.05$ 05 to Test the Claim That

question 94

Multiple Choice

Solve the problem.
-The table shows the number of pitchers with E.R.A's below 3.5 in a random sample of sixty pitchers from the National League and in a random sample of fifty-two pitchers from the American League. Assume that you
Plan to use a significance level of $\alpha = 0.05$ 05 to test the claim that $\mathrm { p } 1 \neq \mathrm { p } 2$ Find the critical value(s) for this
Hypothesis test. Do the data support the claim that the proportion of National League pitchers with an E.R.A.
Below 3.5 differs from the proportion of American League pitchers with an E.R.A. below 3.5? $\begin{array}{lcc}\hline & \text { National League } & \text { American League } \\\hline \text { Number of pitchers in sample } & 60 & 52 \\\text { Number of pitchers with E.R.A. below 3.5 } & 10 & 8 \\\hline\end{array}$

• A) \(z = \pm 1.96\); no
• B) \(z = \pm 2.575\); no
• C) \(z = \pm 1.645\); yes
• D) \(z = 1.645 ;\) yes

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Definitions:

Heart Rate

The number of heartbeats per unit of time, typically expressed in beats per minute (BPM), which can vary with physical activity, emotional states, and overall health conditions.

Upper Respiratory

Pertaining to the upper part of the respiratory system, including the nose, nasal passages, throat (pharynx), and voice box (larynx).

Biofeedback

A therapeutic technique that uses electronic monitoring to convey information about physiological processes, enabling an individual to gain control over bodily functions.

Tension Headaches

A common type of headache characterized by a feeling of tightness around the forehead or back of the head and neck.