The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a random sample of 14 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 32 centimeters and 11 centimeters, respectively. Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated begonias, μ, is different from that reported in the journal? Use the 0.10 level of significance.Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. A. Find the value of the test statistic and round to 3 or more decimal places. (I have posted a picture of an example problem and the equation to use, with the correct answer as every expert I have asked thus far has gotten this problem wrong.) B. Find the critical values. (Round to three or more decimal places.) C. Can it be concluded that the mean height of treated Begonias is different from that reported in the journal? (yes or no)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a random sample of 14 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 32 centimeters and 11 centimeters, respectively. Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated begonias, μ, is different from that reported in the journal? Use the 0.10 level of significance.Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places.

A. Find the value of the test statistic and round to 3 or more decimal places. (I have posted a picture of an example problem and the equation to use, with the correct answer as every expert I have asked thus far has gotten this problem wrong.)

B. Find the critical values. (Round to three or more decimal places.)

C. Can it be concluded that the mean height of treated Begonias is different from that reported in the journal? (yes or no)

Based on their records, a hospital claims that the proportion, p, of full-term babies born weigh over 7 pounds is 47%. A pediatrician who works with several
hospitals in the community would like to verify the hopital's claim and investigates. In a random sample of 210 babies born in the community, 116 weighed
over 7 pounds. Is there enough evidence to reject the hospital's claim at the 0.05 level of significance?
Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)

Finding the value of the test statistic
The value of this test statistic is the z-value corresponding to the sample proportion under the assumption that H is true. Here is its value.
р-р
p(1-p)
n
58
105
-0.47
0.47(1-0.47)
210
~2.392

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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