Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.
-The principal randomly selected six students to take an aptitude test. Their scores were: $\begin{array} { l l l l l l } 81.4 & 78.6 & 71.3 & 77.8 & 76.9 & 77.7 \end{array}$
Determine a $90 \%$ confidence interval for the mean score for all students.
A) $80.11

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.
-The principal randomly selected six students to take an aptitude test. Their scores were: $\begin{array} { l l l l l l } 81.4 & 78.6 & 71.3 & 77.8 & 76.9 & 77.7 \end{array}$
Determine a $90 \%$ confidence interval for the mean score for all students.
A) $80.11 < \mu < 74.45$
B) $80.01 < \mu < 74.55$
C) $74.55 < \mu < 80.01$
D) $74.45 < \mu < 80.11$

Quizplus · Accepted Answer

The sample mean is 77.95 and the sample standard deviation is approximately 3.57. Using a t-distribution with 5 degrees of freedom, the 90% confidence interval is calculated as 77.95 ± 3.40, which results in the interval (74.55, 80.01).

Use the Given Degree of Confidence and Sample Data to Construct