Measuring 25 of FR Electronics's smallest capacitors, you got \(\bar{c}=49.19 \mu \mathrm{F}\) and sample standard deviation \(s_{c}=2.15 \mu \mathrm{F}\). Assume the capacitances follow a Normal distribution \(\phi_{(\mu, \sigma)}\), and determine, with significance \(\alpha=0.02\) and neutral prior, the alternative hypothesis that the mean \(\mu\) is less than \(50 \mu \mathrm{F}\).