Farmer McGregor is now growing carrots in a field. He is particularly interested in veight of his plants at harvesting. Let X denote the weight (g) of a carrot in McGregor's fie Assume X N(200, 400). 1) The farmer has randomly sampled 16 plants. What is the probability that the mean of a rand

New York is known as "the city that never sleeps." A random sample of 25 New Yorkers were asked how much sleep they get per night and the sample mean was 7.3 hours. To test if New Yorkers sleep less than 8 hours a night on average (Ho: u = 8 v.s. HA: u < 8, where u is the mean number of hours New Yorkers sleep a night), the P-value is (i) the probability of getting a random sample of 25 New Yorkers that on average sleep 7.3 hours a night, when New Yorkers actually sleep less than 8 hours per night on average. (ii) the probability of getting a random sample of 25 New Yorkers that on average sleep 7.3 hours or less a night, when New Yorkers actually sleep 8 hours per night on average. (iii) the probability that New Yorkers on average sleep 8 hours per night, given that the 25 randomly sampled New Yorkers on average sleep 7.3 hours a night (iv) the probability that New Yorkers on average sleep less than 8 hours per night, given that the 25 randomly sampled New Yorkers on average sleep 7.3…

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).t Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and o = 0.96 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is µ = 4.80 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.80 grams? Use a = 0.10. (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? O Ho: H 4.8 g; right-tailed O Ho: H = 4.8 g; H1: µ < 4.8 g; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of…

Suppose the horses in a large stable have a mean weight of 818 lbs, and a variance of 3481. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 18 lbs if 34 horses are sampled at random from the stable? 0.920 0.925 0.912 O 0.945 None of these t

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