Question

overtime hours worked a random sample of 16 registered nurses in a large hospital showed that they worked on average 42.7 hours per week. the standard deviation of the sample was 2.3. estimate the mean of the population with 95% confidence. assume the variable is normally distributed. round intermediate answers to at least three decimal places. round your final answers to one decimal place.
$\square < \mu < \square$

Explanation:

Step1: Identify key values

Sample size $n=16$, sample mean $\bar{x}=42.7$, sample standard deviation $s=2.3$, confidence level 95%.

Step2: Find t-critical value

Degrees of freedom $df=n-1=15$. For 95% confidence, $t_{0.025,15}=2.131$.

Step3: Calculate standard error

Standard error $SE=\frac{s}{\sqrt{n}}=\frac{2.3}{\sqrt{16}}=0.575$.

Step4: Compute margin of error

Margin of error $E=t \times SE=2.131 \times 0.575≈1.225$.

Step5: Determine confidence interval

Lower bound: $42.7 - 1.225≈41.5$; Upper bound: $42.7 + 1.225≈43.9$.

Answer:

41.5 < μ < 43.9