Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \underset { 1 } { 2 } = \sigma _{ 2 } ^{ 2 }$ $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 8 & \mathrm { n } _ { 2 } = 7 \
\overline { \mathrm { x } } 1 = 4.1 & \overline { \mathrm { x } } 2 = 5.5 \
\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 2.51
\end{array}$$
A)(-3.406, 0.606)
B)(-1.132, 1.543)
C)(-1.679, 1.987)
D)(2.112, 2.113)

Question

Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \underset { 1 } { 2 } = \sigma _{ 2 } ^{ 2 }$ $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 8 & \mathrm { n } _ { 2 } = 7 \
\overline { \mathrm { x } } 1 = 4.1 & \overline { \mathrm { x } } 2 = 5.5 \
\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 2.51
\end{array}$$
A)(-3.406, 0.606)
B)(-1.132, 1.543)
C)(-1.679, 1.987)
D)(2.112, 2.113)

Quizplus · Accepted Answer

The correct confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ can be calculated using the formula for the difference between two means, assuming equal variances. Given the sample sizes, means, and standard deviations, and using a t-distribution (since the population standard deviations are unknown and the sample sizes are small), the calculation leads to the interval (-3.406, 0.606). This interval is calculated by finding the standard error of the difference between the two means, determining the appropriate t-value for a 95% confidence level and degrees of freedom (which in this case would be the smaller of $n_1 - 1$ and $n_2 - 1$), and then using these to find the margin of error and the confidence interval around the difference in sample means.

Construct a 95% Confidence Interval For μ1−μ2\mu _ { 1 } - \mu _ { 2 }μ1​−μ2​

Construct a 95% Confidence Interval For $\mu _ { 1 } - \mu _ { 2 }$