Answered: According to a report done by S & J…

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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According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 43 months. A researcher for a consumer advocate group tests this by selecting 20 bulbs at random. For the bulbs in the sample, the mean lifetime is 45 months. It is known that the population standard deviation of the lifetimes is 7 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the population mean lifetime, μ, of light bulbs made by this manufacturer differs from 43 months?Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below.

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 p-value

C. Can we conclude that the population mean lifetime of light bulbs made by this manufacturer differs from 43 months? (yes or no)

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

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.)

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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