Question

In: Statistics and Probability

1. Rangers took a random sample of live aspen trees and measured the base circumference of...

1. Rangers took a random sample of live aspen trees and measured the base circumference of each tree. The sample had 50 trees with a mean circumference of 15.57 inches.
a. Find a 95% confidence interval for the population mean base circumference of all aspen trees in Roosevelt National Forest. Assume that the population standard deviation is 4.78 inches. You must show work for full credit.
b. Would the 90% confidence interval for the population mean base circumference of aspen trees be wider or narrower than the 95% confidence interval you found in part A? Explain.

please show complete work, thank you

Solutions

Expert Solution


Related Solutions

In Roosevelt National Forest the rangers took random samples of live aspen trees (Populus tremuloides) and...
In Roosevelt National Forest the rangers took random samples of live aspen trees (Populus tremuloides) and measured the base circumference of each tree. Assume these measurements are normally distributed. (a) The first sample had 30 trees with a mean circumference of 15.71 inches and a sample standard deviation of 4.63 inches. Find a 95% confidence interval for the mean circumference of aspen trees from these data. (b) The next sample had 90 trees with a mean of 15.58 inches and...
1. As part of an environmental studies class project, students measured the circumference of a random sample of 45 blue spruce trees near Brainard Lake, Colorado.
Please show all work, step by step: a. The critical value b. the error bound c. The minimum and maximum numbers of the interval. On interpretations include information about the specific problem. 1.   As part of an environmental studies class project, students measured the circumference of a random sample of 45 blue spruce trees near Brainard Lake, Colorado. The sample mean circumference was x = 29.8 inches. Assume that o is known to be 7.2 inches. a. Find a 90%...
1. A forester measured a sample of trees in a tract of land being sold for...
1. A forester measured a sample of trees in a tract of land being sold for a lumber harvest. Among 27 trees, she found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose her sample gives an accurate representation of the entire tract of land and that the tree diameters follow a normal distribution. Round to 2 decimal places, when applicable. (a) Sketch a graph of the distribution of tree diameters, labeling the mean and...
3) A random sample of 100 pumpkins is obtained and the mean circumference is found to...
3) A random sample of 100 pumpkins is obtained and the mean circumference is found to be 40.5 cm. Assuming that the population standard deviation is known to be 1.6 cm, use a 0.05 significance level to test the claim that the mean circumference of all pumpkins is equal to 39.9 cm.
1.The cholesterol levels of a random sample of 100 men are measured. The sample mean is...
1.The cholesterol levels of a random sample of 100 men are measured. The sample mean is 188 and the sample standard deviation is 40. Which of the following provides a 95% confidence interval for the population mean? A.188 ± (1.96)(40) B.188 ± (1.96)(4) C.188 ± (1.96)(400) D.188 ± (1.96)(0.4)   2.The cholesterol levels of a random sample of 100 men are measured. The sample mean is 188 and the sample standard deviation is 40. Which of the following provides a 99%...
Researchers interested in the trees of a forest in Vermont selected a random sample of 8...
Researchers interested in the trees of a forest in Vermont selected a random sample of 8 red oak trees and measured various characteristics of these trees. Here are the heights of the trees, in feet: 32, 48, 35, 51, 46, 30, 28, 39 In a study done several years earlier the average height of red oak trees in this forest was reported to be 35 feet. The researchers claim that the average height is now greater than 35 feet. Test...
A random sample of 24 chemical solutions is obtained, and their strengths are measured. The sample...
A random sample of 24 chemical solutions is obtained, and their strengths are measured. The sample mean is 5437.2 and the sample standard deviation is 376.9. (a) Construct a two-sided 98% confidence interval for the average strength. (b) Estimate how many additional chemical solutions need to be measured in order to obtain a twosided 98% confidence interval for the average strength within a margin of error that is 150
In a local university, 40% of the students live in the dormitories. A random sample of...
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is Select one: a. 0.0336 b. 0.9664 c. 0.9328 d. 0.4664
1)In a sample of 300 trees on someone’s orchard, A proportion of 0.78 were peach trees....
1)In a sample of 300 trees on someone’s orchard, A proportion of 0.78 were peach trees. Construct a 90% confidence interval for the total population proportion of peach trees in the entire orchard 2) Suppose A is the lower bound of the confidence interval you calculated in the previous problem. If you instead calculated a 99% confidence interval, would your lower bound be less than A or greater than A?
I took a sample of 20 students at St. Kate’s and measured their heights. I computed...
I took a sample of 20 students at St. Kate’s and measured their heights. I computed the sample mean (x bar) and want to construct a confidence interval. I want to create an approximate 95% confidence interval. What is this? I took a sample of 20 students and recorded their height. X bar (sample mean) was 63 inches. The population standard deviation for height is 4 inches. What is the approximate 95% confidence interval? A 99% confidence interval will always...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT