Question

math - part 1
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01

based on these estimates and margin of error, which of the following is the most appropriate conclusion about the proportions of different materialspresent in the sand?
a the proportion of organic matter will be lower than the proportion of basalt
b the proportion of gamet will be lower than the proportion of organic matter.
c the proportion of garnet will be greater than 0.
d the proportion of quartz will be greater than 0.61

Explanation:

Step1: Analyze Option A

The proportion of organic matter is \(0.12\) and basalt is \(0.19\). But with margin of error, we can't be sure. For example, if organic matter's upper limit and basalt's lower limit overlap, we can't conclude.

Step2: Analyze Option B

Garnet is \(0.01\) and organic matter is \(0.12\). But with margin of error, if garnet's upper limit and organic matter's lower limit overlap, we can't be sure.

Step3: Analyze Option C

Garnet's proportion is \(0.01\). But with margin of error, if the margin of error is such that the lower limit could be \(0\) (e.g., if margin of error is \(0.01\), then \(0.01 - 0.01=0\)), we can't be sure.

Step4: Analyze Option D

Assume a common margin of error (say \(0.07\) for example, since it's a common value in such problems). The lower limit of quartz proportion: \(0.68-0.07 = 0.61\). So the proportion of quartz will be greater than \(0.61\) (because the lower - bound of its confidence interval is \(0.61\)).

Answer:

D. The proportion of quartz will be greater than \(0.61\)