Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Assume the two samples are random and independent. The sample statistics are given below.
Population statistics: $\sigma _ { 1 } = 2.5 \text { and } \sigma _ { 2 } = 2.8$ Sample statistics: $\overline { \mathrm { x } } 1 = 12 , \mathrm { n } _ { 1 } = 40 \text { and } \overline { \mathrm { x } } 2 = 13 , \mathrm { n } _ { 2 } = 35$
A)(-2.209, 0.209)
B)(-2.001, -1.873)
C)(-1.968, 1.561)
D)(-1.673, 1.892)

Question

Quizplus · Accepted Answer

The correct answer is A because the confidence interval is calculated as:$\overline { \mathrm { x } } 1 - \overline { \mathrm { x } } 2 \pm z _ { \alpha / 2 } \sqrt { \frac { \sigma _ { 1 } ^ { 2 } } { \mathrm { n } _ { 1 } } + \frac { \sigma _ { 2 } ^ { 2 } } { \mathrm { n } _ { 2 } } }$where $z _ { \alpha / 2 } $ is the critical value from the standard normal distribution with a significance level of $\alpha / 2$.Plugging in the given values, we get:$12 - 13 \pm 1.96 \sqrt { \frac { 2.5 ^ { 2 } } { 40 } + \frac { 2.8 ^ { 2 } } { 35 } }$$= -1 \pm 1.96 \sqrt { 0.15625 + 0.21857 }$$= -1 \pm 1.96 \sqrt { 0.37482 }$$= -1 \pm 1.96 (0.6122)$$= -1 \pm 1.209$Therefore, the 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ is $(-2.209, 0.209)$.

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

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