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).

95 | 86 | 84 | 107 | 99 | 112 | 84 | 87

The sample mean isx94.3. Letxbe a random variable representing glucose readings taken from Gentle Ben. We may assume thatxhas a normal distribution, and we know from past experience that= 12.5.The mean glucose level for horses should be= 85 mg/100 ml.

Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use= 0.05.

(a) What is the level of significance?

(b) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

• H₀:= 85;H₁:> 85; right-tailed
• H₀:= 85;H₁:85; two-tailed
• H₀:> 85;H₁:= 85; right-tailed
• H₀:= 85;H₁:< 85; left-tailed

(c)What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

• 1. The Student'st, sincenis large with unknown.
• 2. The Student'st, since we assume thatxhas a normal distribution with known.
• 3. The standard normal, since we assume thatxhas a normal distribution with unknown.
• 4. The standard normal, since we assume thatxhas a normal distribution with known.

(d) Compute thezvalue of the sample test statistic. (Round your answer to two decimal places.)

(e) Find (or estimate) theP-value. (Round your answer to four decimal places.)

(f) Sketch the sampling distribution and show the area corresponding to theP-value.

(g) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

• 1. At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
• 2. At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
• 3. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
• 4. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application.

• There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.
• There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.