Question

is there a doctor in the house? a market research firm reported the mean annual earnings of all family practitioners in the united states was $178,258. a random sample of 44 family practitioners in los angeles had mean earnings of \LXI0 with a standard deviation of $41,407. do the data provide sufficient evidence to conclude that the mean salary for family practitioners in los angeles differs from the national average? use the \\( \alpha = 0.01 \\) level of significance and the p - value method and excel. \
part: 0 / 5 \
part 1 of 5 \
(a) state the appropriate null and alternate hypotheses. \
\\( h_0: \\) \
\\( h_1: \\) \
this hypothesis test is a \\( \boxed{\text{select}} \\) test.

Explanation:

Step1: Define Null Hypothesis

The null hypothesis \( H_0 \) is a statement of no difference or equality. Here, we test if the mean salary in Los Angeles (\(\mu\)) is equal to the national average (\(178258\)). So \( H_0: \mu = 178258 \).

Step2: Define Alternate Hypothesis

The alternate hypothesis \( H_1 \) is what we suspect might be true. The problem asks if the mean differs from the national average, so it's a two - tailed test. Thus, \( H_1: \mu
eq178258 \).

Step3: Identify Test Type

Since we know the population standard deviation (or here we use the sample standard deviation as an estimate? Wait, actually, the problem gives a sample standard deviation? Wait, no, the market research firm reported the mean annual earnings of all family practitioners (population mean?) Wait, the problem says "the mean annual earnings of all family practitioners in the United States was \$178,258". So that's the population mean \(\mu_0 = 178258\). We have a sample of \( n = 44 \), sample mean \( \bar{x}=193250 \), sample standard deviation \( s = 41407 \). Since the sample size \( n = 44\) is large (\(n\geq30\)), we can use a z - test (or t - test, but for large \(n\), z and t are close). But the key is the hypothesis: \( H_0:\mu = 178258 \), \( H_1:\mu
eq178258 \), and it's a two - tailed test.

Answer:

\(H_0:\mu = 178258\)

\(H_1:\mu
eq178258\)

This hypothesis test is a two - tailed test.