Assignment:
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 89 83 104 99 111 85 91
The sample mean is x = 94.4. 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. Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use alpha = 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
H0: mu = 85; H1: mu is not equal to 85; two-tailed H0: mu = 85; H1: mu > 85; right-tailed H0: mu = 85; H1: mu < 85;="" left-tailed="" h0:="" mu=""> 85; H1:mu = 85; right-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since we assume that x has a normal distribution with known sigma. The Student's t, since n is large with unknown sigma. The standard normal, since we assume that x has a normal distribution with unknown sigma. The Student t, since we assume that x has a normal distribution with known sigma.
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.)
Sketch the sampling distribution and show the area corresponding to the P-value.