Let S and S denote the variances of random samples, of sizes n and m respectively, from two independent distributions which are N(u1,o²) and N(µ2, 0²), respectively. Note that the two populations have different means but the same variances. You may use the fact that has the distribution x with (n + m – 2) df o2 to help you to find a confidence interval for the common unknown variance o?.

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Let S and S denote the variances of random samples, of sizes n and m respectively, from
two independent distributions which are N(u1,02) and N(u2, 02), respectively. Note that
the two populations have different means but the same variances. You may use the fact that
nSỉ + mS?
has the distribution x? with (n + m – 2) df
o2
to help you to find a confidence interval for the common unknown variance o².
Transcribed Image Text:Let S and S denote the variances of random samples, of sizes n and m respectively, from two independent distributions which are N(u1,02) and N(u2, 02), respectively. Note that the two populations have different means but the same variances. You may use the fact that nSỉ + mS? has the distribution x? with (n + m – 2) df o2 to help you to find a confidence interval for the common unknown variance o².
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