Question

the average scores for 25 participants is 55, with a sd of 9.1
calculate the 95 % confidence interval. enter the lower boundary of the interval.
a. 50.341
b. 58.756
c. 51.396
d. 51.244

Explanation:

Step1: Identify given values

Sample size $n=25$, sample mean $\bar{x}=55$, sample standard deviation $s=9.1$, confidence level $95\%$

Step2: Find critical t-value

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

Step3: Calculate standard error

$\text{SE}=\frac{s}{\sqrt{n}}=\frac{9.1}{\sqrt{25}}=\frac{9.1}{5}=1.82$

Step4: Compute margin of error

$\text{ME}=t^*\times\text{SE}=2.064\times1.82=3.75648$

Step5: Find lower boundary

$\text{Lower Bound}=\bar{x}-\text{ME}=55-3.75648$

Answer:

a. 50.341