many ground level plants in tropical rainforest have adapted to the shade of the forest canopy. these plants tend to function well as house plants since they require minimal sunlight. A botanist is interested in domesticating a particular plant found in the amazon rainforest. The botanist wants to estimate the true proportion of this species of plant that will survive inside. assuming an appropriate sample can be obtained, which confidence interval would be most appropriate for this task?
Confidence interval for one proportion
To estimate the true proportion of a species of plant that will survive inside as houseplants, the most appropriate confidence interval for this task would be a confidence interval for proportions.
The reason is that the botanist is interested in estimating the proportion of plants that will survive as houseplants, which is a categorical variable. The proportion of survival will be a proportion of the sample that will give an estimate of the true proportion in the population.
A confidence interval for proportions is used to estimate the range of likely values for a population proportion based on a sample. It provides an interval estimate of the unknown population proportion and gives an indication of the uncertainty associated with the estimate.
Therefore, the botanist should use a confidence interval for proportions to estimate the true proportion of this species of plant that will survive inside as houseplants.
To estimate the true proportion of the species of plant that will survive inside, the botanist can use a confidence interval for a proportion. This type of confidence interval is used when estimating the proportion or percentage of a population that possesses a certain characteristic. In this case, the characteristic is whether the plant survives inside.
To construct a confidence interval for a proportion, the botanist needs to follow these steps:
1. Sample Selection: The botanist should obtain an appropriate sample of the plant species found in the Amazon rainforest. The sample should be representative of the population of interest.
2. Sample Size: Determine the appropriate sample size needed for the confidence interval. This can be determined using statistical calculators or formulas, taking into consideration factors such as desired confidence level, margin of error, and anticipated population proportion.
3. Data Collection: Collect data on whether each plant in the sample survived inside or not.
4. Calculate Sample Proportion: Calculate the proportion of plants that survived inside from the collected data. This is done by dividing the number of plants that survived inside by the total number of plants in the sample.
5. Confidence Interval Calculation: Use statistical methods to calculate the confidence interval for the proportion. The most common method is based on the normal distribution, assuming certain conditions are met (such as a sufficiently large sample size).
6. Interpretation: Finally, interpret the confidence interval obtained. For example, a 95% confidence interval means that if the procedure is repeated many times, approximately 95% of these intervals would contain the true proportion of plants that survive inside.
Therefore, for the botanist's task of estimating the true proportion of the species of plant that will survive inside, the most appropriate confidence interval to use is a confidence interval for a proportion.