Question

1. A researcher believes that the mean age of medical doctors in a large hospital is older than the average of doctors in the United States, which is 46. Assume the population standard deviation is 4.2 years. A random sample of 30 doctors from the system is selected, and the mean age of the sample is 48.6. Test the claim at a =0.01. (12 points → 2 points for each step) Show all steps. Step 1: State the question of concern (claim). Step 2: State the hypotheses (Ho and Ha)→ Identify which is the claim. (1 extra pt. for claim) Step 3: Identify the critical region. Step 4: Compute the test statistic. Step 5. Make a decision to reject or not reject the null hypothesis Ho. Step 6: Make a conclusion regarding the claim and decision.

Answer 1

1.

Whether the mean age of medical doctors in a large hospital is more than the average of doctors in the united states.

2.

H_o: or the mean age of medical doctors in a large hospital is same as that of the average of doctors in the united states.

u= 46

H₁:$\mu>46$ or the mean age of medical doctors in a large hospital is more than the average of doctors in the united states.

3.

Based on the information provided, the significance level is \alpha = 0.01α=0.01, and the critical value for a right-tailed test is zc​=2.33

The rejection region for this right-tailed test is R={z:z>2.33}

4.

Test Statistics

The z-statistic is computed as follows:

$z = \frac{\bar X - \mu_0}{\sigma/\sqrt{n}} = \frac{ 48.6 - 46}{ 4.2/\sqrt{ 30}} = 3.391$

5.

Since it is observed that z=3.391>zc​=2.33, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0003, and since p=0.0003<0.01, it is concluded that the null hypothesis is rejected.

6.

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 46, at the 0.01 significance level or the mean age of medical doctors in a large hospital is more than the average of doctors in the united states.

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