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 88 82 103 100 108 84 87   The sample mean is x ≈ 93.4. 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 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. (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: μ = 85; H1: μ > 85; right-tailedH0: μ > 85; H1: μ = 85; right-tailed    H0: μ = 85; H1: μ ≠ 85; two-tailedH0: μ = 85; H1: μ < 85; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with unknown σ.The standard normal, since we assume that x has a normal distribution with unknown σ.    The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since we assume that x has a normal distribution with known σ. 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.)

The following information is slightly different for each student but very close to the actual real data. Assume the number of years in prison before being exonerated is normally distributed for both white and black males. The average amount of time Black males are in prison before being exonerated is 13.7 years with a population standard deviation of 9.8 years. The average amount of time White male are in prison before being exonerated is 9.2 years with a population standard deviation of 8.6. Give all answers to at least 2 decimal places.a) If a Black male is at the 70th percentile for years in prison before being exonerated, find the time the person has been in prison. years

An investigation of the relationship between traffic flow (measured in cars per day) and lead content (measured in micrograms per gram of dry weight) in the bark of trees near the highway yielded the following summary statistics:   Sample Mean Sample Standard Deviation Lead Content (micrograms per gram dry weight) 680 240 Traffic Flow (cars / day) 1750 800 The correlation between lead content and traffic flow was found to be r = 0.6 and a scatterplot showed the form to be linear.   Based on context, which is the X-variable and which is the Y-variable? Group of answer choices X-variable                                                                 Y-variable

Assume the population is normally distributed