Question: #10: Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).

93 88 82 105 99 110 84 89

The sample mean is \(\bar{X}\) = 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that \(\sigma \) = 12.5. The mean glucose level for horses should be \(\mu \) = 85 mg/100 ml (Reference: Merck Veterinary Manual). Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use \(\alpha \) = 0.05.