Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a

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). 95 87 80 103 97 110 85 89 The sample mean is x 93.3. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we kr 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? .05 State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H_0: mu > 85; H_1 mu = 85; right-tailed H_0: mu = 85; H_1: mu > 85; right-tailed H_0: mu = 85; H_1 mu + 85; two-tailed H_0: mu = 85; H_1: mu

Explanation / Answer

Solution:-

a) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: < 85

Alternative hypothesis: > 85

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE),and the z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 4.42

z = (x - ) / SE

z = 1.88

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a z statistic test statistic of 1.88. We use the normal Distribution Calculator to find P(z > 1.88) = 0.0301

Interpret results. Since the P-value (0.03) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that Gentle Bin has overall level glucose higher than 85.

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