Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

Multiple Choice

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-When performing a hypothesis test for the ratio of two population variances, the upper critical $F$ value is denoted $\mathrm { F } _ { \mathrm { R } }$ . The lower critical $\mathrm { F } _ { \text {value, } } \mathrm { F } _ { \mathrm { L } }$ , can be found as follows: interchange the degrees of freedom, and then take the reciprocal of the resulting $\mathrm { F }$ value found in table $\mathrm { A } - 5$ . $\mathrm { F } _ { \mathrm { R } }$ can be denoted $\mathrm { F } _ { \alpha / 2 }$ and $\mathrm { F } _ { \mathrm { L } }$ can be denoted $\mathrm { F } _ { 1 - \alpha / 2 }$ .
Find the critical values $\mathrm { F } _ { \mathrm { L } }$ and $\mathrm { F } _ { \mathrm { R } }$ for a two-tailed hypothesis test based on the following values:
$$\mathrm { n } _ { 1 } = 10 , \mathrm { n } _ { 2 } = 16 , \alpha = 0.05$$

A) $0.2653,3.1227$
B) $3.1227,3.7743$
C) $0.2653,3.7743$
D) $0.3202,3.1227$