he heights of a certain population of corn plants are assumed to follow a normal distribution. Nine plants were chosen at random from the population. The heights in meters were as follows. 1.40, 1.30, 1.36, 1.38, 1.40, 1.20, 1.52, 1.70, 1.95 (a) What is the sample mean of the nine plants? (b) What is the sample standard deviation? (c) What is the standard error of the mean? (d) Construct a 90% confidence interval for the population mean height. (e) Construct a 90% confidence interval for the population standard deviation. (f) What is the estimate of ?p, the population proportion of corn plants that are shorter than 1.40m? (g) Suppose we are interested in p, the true proportion of corn plants shorter than 1.40m. How large should the sample size n of a new study be such that the margin of error does not exceed 3% at the 95% level of confidence? In the following, assume that the population distribution of heights is normal with mean 1.45 meters and standard deviation 0.22 meters. (h) For a plant selected at random from this population, what is the probability that its height is between 1.30m and 1.50m? (i) If a random sample of size n=4 is taken, what is the probability that the sample mean height is between 1.30m and 1.50m?
The heights of a certain population of corn plants are assumed to follow a
1.40, 1.30, 1.36, 1.38, 1.40, 1.20, 1.52, 1.70, 1.95
(a) What is the sample
(b) What is the sample standard deviation?
(c) What is the standard error of the mean?
(d) Construct a 90% confidence interval for the population mean height.
(e) Construct a 90% confidence interval for the population standard deviation.
(f) What is the estimate of ?p, the population proportion of corn plants that are shorter than 1.40m?
(g) Suppose we are interested in p, the true proportion of corn plants shorter than 1.40m. How large should the sample size n of a new study be such that the margin of error does not exceed 3% at the 95% level of confidence?
In the following, assume that the population distribution of heights is normal with mean 1.45 meters and standard deviation 0.22 meters.
(h) For a plant selected at random from this population, what is the probability that its height is between 1.30m and 1.50m?
(i) If a random sample of size n=4 is taken, what is the probability that the sample mean height is between 1.30m and 1.50m?
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