Question

select the correct null and alternate hypothesis
a random sample of 49 medical doctors in la showed that they worked an average of 53.1 hours/week with a
standard deviation of 7.2 hours/week. if the california average is 60 hours/week, does this give evidence that
the la doctors work significantly less than the rest of california?
ho: p = 60
ha: p < 60
ho: μ = 53.1
ha: μ < 53.1
ho: μ = 60
ha: μ < 60
none of these

Explanation:

Step1: Identify the parameter

The problem is about the average working hours of doctors. The parameter of interest is the population mean \(\mu\) (average hours per week).

Step2: Set up the null hypothesis

The null hypothesis \(H_0\) is a statement of no difference. Here, we are comparing the average hours of LA doctors to the California average. The California average is given as 60 hours/week. So, \(H_0:\mu = 60\).

Step3: Set up the alternative hypothesis

The alternative hypothesis \(H_a\) is the claim we are testing. The claim is that LA doctors work significantly less than the California average. So, \(H_a:\mu<60\).

Answer:

\(H_0:\mu = 60\), \(H_a:\mu<60\) (the third option in the given choices)