Question

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

87

83

107

101

110

83

89

The sample mean is x ≈ 94.1. 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 σ = 12.5. The mean glucose level for horses should be μ = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use α = 0.05.

(a) What is the level of significance?
(b)Compute the z value of the sample test statistic. (Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Answer 1

a) Level of significance = 0.05

b) test statistic Z is

  

Z = ( xbar - )//√n

Z = 94.1 - 85 /12.5/√8

Z = 2.06

This is test statistic value

c) The p-value for z = 2.06 and right tailed is

P-value = P ( Z > 2.06)

= 1 - P ( z < 2.06)

= 1 - 0.9803

P -value = 0.0197

Here p-value < 0.05 , so we reject the null hypothesis H0.

Conclusion : There is sufficient evidence to support the claim that Gentle man has an overall average glucose level is higher than the 85