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.\
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part: 0 / 5\
\
part 1 of 5\
(a) state the appropriate null and alternate hypotheses.\
\\(h_0: \mu = 178258\\)\
\\(h_1: \mu \
eq 178258\\)\
this hypothesis test is a two - tailed test.\
\
part: 1 / 5\
part 2 of 5\
(b) compute the value of the test statistic. round the answer to at least three decimal places.\
\\(t = 2.402\\)\
\
part: 2 / 5\
part 3 of 5\
find the \\(p\\)-value. round the answer to at least four decimal places.\
\\(p\\)-value = 0.0206\
\
part: 3 / 5\
part 4 of 5\
determine whether to reject \\(h_0\\).\
select the null hypothesis \\(h_0\\).

Explanation:

Step1: Recall Rejection Rule

For a hypothesis test, we reject \( H_0 \) if \( P\text{-value} < \alpha \). Here, \( \alpha = 0.01 \) and \( P\text{-value} = 0.0206 \).

Step2: Compare P - value and α

Compare \( 0.0206 \) and \( 0.01 \). Since \( 0.0206>0.01 \), we do not reject \( H_0 \).

Answer:

Do not reject the null hypothesis \( H_0 \).