Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.
-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. The mean fee charged by the clinic for a random sample of 65 patients receiving this procedure was $1280. Test whether the claim that the mean fee charged by this particular clinic is higher than $1200 is supported or not supported. Assume that $\sigma = \$ 210$
A)not supported
B)supported

Question

Quizplus · Accepted Answer

The hypothesis test is a one-tailed test where the null hypothesis ($H_0$) is that the mean fee ($\mu$) is $1200, and the alternative hypothesis ($H_a$) is that the mean fee is greater than $1200. The test statistic is calculated using the formula $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean under the null hypothesis, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values, we get $z = \frac{1280 - 1200}{210/\sqrt{65}} \approx 2.77$. At the 0.05 significance level, the critical z-value for a one-tailed test is approximately 1.645. Since 2.77 > 1.645, we reject the null hypothesis and support the claim that the mean fee charged by the clinic is higher than $1200.

Conduct a Full Hypothesis Test and Determine If the Given σ=$210\sigma = \$ 210σ=$210

Conduct a Full Hypothesis Test and Determine If the Given $\sigma = \$ 210$