Question

lets say were aiming to assess the average time in minutes spent on a specific task each week by employees in a company. to gather data, we randomly select a group of 25 employees, and we determine the average time spent on the task in minutes based on this sample was 6.5 with a sd of 7.6.
calculate the lower bound of the 95% confidence interval.
include at least 3 decimal places.
○ a. 3.521
○ b. 3.363
○ c. 9.479
○ d. 9.637

Explanation:

Step1: Identify key values

Sample size $n=25$, sample mean $\bar{x}=6.5$, sample SD $s=7.6$, confidence level 95%

Step2: Find t-critical value

Degrees of freedom $df=n-1=24$. For 95% confidence, $t^*=2.064$

Step3: Calculate standard error

$\text{SE}=\frac{s}{\sqrt{n}}=\frac{7.6}{\sqrt{25}}=\frac{7.6}{5}=1.52$

Step4: Compute margin of error

$ME=t^*\times\text{SE}=2.064\times1.52=3.13728$

Step5: Calculate lower bound

$\text{Lower Bound}=\bar{x}-ME=6.5-3.13728$

Answer:

b. 3.363