A researcher collects the following weights in grams of dimes minted after $2000:2.312,2.284,2.298,2.315,2.289,2.301,2.307,2.294,2.319,2.288$. Construct a $95\%$ confidence interval estimate of the mean weight of all dimes minted after $2000$. The official specification requires a weight of $2.268$ grams. Does the confidence interval suggest the mean meets the specification?

$(2.292\text{ grams},2.309\text{ grams})$, the confidence interval suggests the mean meets the specification

$(2.292\text{ grams},2.309\text{ grams})$, the confidence interval suggests the mean does not meet the specification

$(1.292\text{ grams},1.309\text{ grams})$, the confidence interval suggests the mean meets the specification

$(1.292\text{ grams},1.309\text{ grams})$, the confidence interval suggests the mean does not meet the specification