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Answer :
The correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams
What Is a Confidence Interval?
A confidence interval, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.
What is a 95% confidence interval?
A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.
How to find the correct interpretation of this interval?
Since the 95% confidence interval for the mean weight of apples in an orchard at a specific given time is between 147 grams to 151 grams.
This follows that from our definition of confidence interval and 95 % confidence interval, that there is a 95 % confidence that the mean weight of the apples in the orchard lies between 147 grams to 151 grams.
So, the correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams
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Final answer:
The correct interpretation of a 95% confidence interval for the mean weight of apples is that there is a 95% confidence that the true population mean weight of all apples in the orchard lies between 147 grams to 151 grams.
Explanation:
The correct interpretation of the 95% confidence interval for the mean weight of apples in an orchard being between 147 grams to 151 grams is option (b): I am 95% confident that the mean weight for all the apples in the orchard will be between 147 grams to 151 grams. This means that if we were to take many samples of apples from the orchard and calculate the confidence interval for each sample, roughly 95% of these intervals would contain the true population mean weight of the apples.
When discussing a confidence interval, it's important to remember that the interval itself gives a range of plausible values for the population mean based on the sample data. The confidence level (95% in this case) indicates how sure we are that the interval contains the true mean, not the likelihood that a single mean or measurement will fall within that interval.
