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 86 83 104 101 108 86 87

The sample mean is x ≈ 93.5. 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.

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.)

(d) 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 α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.  

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

Answer 1

Given : Sample size=n=8

Sample mean=

Population standard deviation=

Significance level=

Hypothesized value=

Since , Population standard deviation= is known but the Sample size=n=8 < 30

Therefore , use Z-test

Claim : The Gentle Ben has an overall average glucose level higher than 85 mg/100 ml.

(a) Hypothesis : Vs

(b) The test statistic is ,

(c) P-value =

(d) Decision : Here , P-value = 0.0274 <

Therefore , reject the null hypothesis.

Conclusion : At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.