Question: How big are tomatoes? Some say that depends on the growing conditions. A random sample of \(n_{1}=89\) organically grown tomatoes had sample mean weight \(\bar{x}_{1}=3.8\) ounces. Another random sample of \(n_{2}=75\) tomatoes that were not organically grown had sample mean weight \(\bar{x}_{2}=4.1\) ounces. Previous studies show that \(\sigma_{1}=0.9\) ounce and \(\sigma_{2}=1.5\) ounces. Does this indicate a difference either way between population mean weights of organically grown tomatoes compared to those not organically grown? Use a \(5 \%\) level of significance.

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