A Hypothesis Testing Situation Is Given $\mu.$ To Draw the Power Curve

question 28

Essay

A hypothesis testing situation is given. The population standard deviation, sample size, and significance level are given.Complete the table to give the probability of a Type II error and the power for each of the given values of µ. Use the table $\mu.$ to draw the power curve.
-A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. Preliminary data analyses indicate that it is reasonable to apply a z-test. The hypotheses are $\begin{array} { l } \mathrm { H } _ { 0 } : \mu = \$ 1200 \\ \mathrm { H } _ { \mathrm { a } } : \mu > \$ 1200 . \end{array}$ Assume that $\sigma = \$ 180 , \mathrm { n } = 38$ , and the significance level is $0.10$ . Find the probability of a Type II error and the power for $\mu = 1190,1200,1210,1220,1230,1240,1250,1260,1270$ , $1280$ , $1290 .$ 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290

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Definitions:

Heart Disease

A broad term for various conditions affecting the heart's structure and function, leading to health complications.

Inflammation

When bodily tissues swell in response to a perceived or real threat.

Swell

A term often used to describe a long wave on the water's surface that has traveled a great distance.

Perceived Threat

The subjective interpretation of a potential harm or danger, influencing an individual's response and behavior towards it.