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). 98, 88, 82, 105, 99, 105, 84, 89 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 = 12.2. An average glucose level for horses is 90 (mg/100 ml). Do these sample data values indicate that Gentle Ben has a mean glucose level higher than 90? Use = 0.01. (a) Enter the following. x = s = (b) Identify the claim, the null hypothesis, and the alternative hypothesis. Claim: 90 Ho: 90 H1: 90 (c) Will you use a left-tailed, right-tailed, or two-tailed test? two-tailed right-tailed left-tailed (d) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since n is large with known . The Student's t, since n is large with unknown . The standard normal, since we assume that x has a normal distribution with unknown . The Student's t, since we assume that x has a normal distribution with known . The standard normal, since we assume that x has a normal distribution with known . The standard normal, since n is large with unknown . (e) Sketch the sampling distribution showing the area corresponding to the approximate P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (f) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (g) State your conclusion in the context of the application. Fail to reject the null hypothesis, there is insufficient evidence that Gentle Ben's glucose is higher than average. Fail to reject the null hypothesis, there is sufficient evidence that Gentle Ben's glucose is higher than average. Reject the null hypothesis, there is insufficient evidence that Gentle Ben's glucose is higher than average. Reject the null hypothesis, there is sufficient evidence that Gentle Ben's glucose is higher than average.

Explanation / Answer

a) HO:mu=90 H1:mu>90

Use Standard normal distribution since, X has a normal distribution, and population standard deviation is known.

b)Z=(Xbar-mu)/(sigma/sqrt n)

=(92.14-90)/(12.2/sqrt 7)

=0.46

The p value is 0.3227.

Fail to reject H0( pvalue i snot less than 0.01), there is insufficient evidence that Gentle Bens glucose is higher than average.

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