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)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.5: Interpreting Data

Problem 4E

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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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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