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 90 84 107 97 108 82 91 The sample mean is x ≈ 94.3. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we 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.   State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: ? = 85; H1: ? ≠ 85; two-tailed H0: ? = 85; H1: ? < 85; left-tailed     H0: ? > 85; H1: ? = 85; right-tailed H0: ? = 85; H1: ? > 85; right-tailed   What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. A) The standard normal, since we assume that x has a normal distribution with unknown ?. B) The Student's t, since we assume that x has a normal distribution with known ?.     C) The Student's t, since n is large with unknown ?. D) The standard normal, since we assume that x has a normal distribution with known ?.   Compute the z value of the sample test statistic. (Round your answer to two decimal places.)   Find (or estimate) the P-value. (Round your answer to four decimal places.)   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 ??   A) At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. B) At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.     C) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. D) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...