A small amount of the trace element selenium, from 50 to 200 micrograms (ug) per day, is considered essential to good health. Suppose that independent random samples of n₁ = n₂ = 30 adults were selected from two regions of the United States, and a day's intake of selenium, from both liquids and solids, was recorded for each person. The mean and standard deviation of the selenium daily intakes for the 30 adults from region 24.3 µg, respectively. The corresponding statistics for 140.9 µg and $₁ 17.6 μg. 1 were ₁ 167.1 µg and $₁ the 30 adults from region 2 were ₂ = = = = a. Find a 95% confidence interval for the difference in the mean selenium intake for the two regions. Interpret the interval. b. Suppose that you wish to estimate the difference in the mean daily intake between the two regions, correct to within 5 µg, with probability 0.90. If you plan to select an equal number of adults from the two regions (thatis, if µ₁ should n₁ and N2 be? M₂), how large =

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n₁ = n₂
A small amount of the trace element selenium, from 50 to 200 micrograms (ug) per day,
is considered essential to good health. Suppose that independent random samples of
30 adults were selected from two regions of the United States, and a day's
intake of selenium, from both liquids and solids, was recorded for each person. The
mean and standard deviation of the selenium daily intakes for the 30 adults from region
24.3 µg, respectively. The corresponding statistics for
17.6 mg.
140.9 µg and $₁
=
si
1 were ₁
167.1 µg and $₁ =
1
the 30 adults from region 2 were ₂
=
=
=
a. Find a 95% confidence interval for the difference in the mean selenium intake for
the two regions. Interpret the interval.
b. Suppose that you wish to estimate the difference in the mean daily intake between
the two regions, correct to within 5 µg, with probability 0.90. If you plan to select
an equal number of adults from the two regions (thatis, if µ1
should n₁ and n₂ be?
M₂), how large
=
Transcribed Image Text:n₁ = n₂ A small amount of the trace element selenium, from 50 to 200 micrograms (ug) per day, is considered essential to good health. Suppose that independent random samples of 30 adults were selected from two regions of the United States, and a day's intake of selenium, from both liquids and solids, was recorded for each person. The mean and standard deviation of the selenium daily intakes for the 30 adults from region 24.3 µg, respectively. The corresponding statistics for 17.6 mg. 140.9 µg and $₁ = si 1 were ₁ 167.1 µg and $₁ = 1 the 30 adults from region 2 were ₂ = = = a. Find a 95% confidence interval for the difference in the mean selenium intake for the two regions. Interpret the interval. b. Suppose that you wish to estimate the difference in the mean daily intake between the two regions, correct to within 5 µg, with probability 0.90. If you plan to select an equal number of adults from the two regions (thatis, if µ1 should n₁ and n₂ be? M₂), how large =
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