The null hypothesis is rejected when the sample mean M is greater than or equal to 68.95 . Therefore, the architectural firm will make thedecision not to open a branch in Vermont if M isless than 68.95(Hint: To use the tool, set the Mean to the hypothesized mean (65) and the Standard Deviation to the standard deviation of the sampling distributionof M.)Suppose that the true value of u is 69 years. The probability that the architecture firm commits a Type II error is 0.4883(Hint: To use the tool, set the Mean to the true mean (69) and position the vertical line at the critical value of M0.010.5000If the true value of µ is 69 years, the power of the test is 0.51990.4801Based on the level of significance it has selected for its test, the architectural firm is willing to risk aunprofitable branch. It is willing to risk a 0.20 probability of not opening the branch when u = 69. (In other words, it is willing to fail to reject the nullhypothesis when it actually should have rejected the null hypothesis only 20% of the time.) What should the firm do?0.010.4883 ty of opening anDecrease its sample size.Decrease a.Increase its sample size.O Do nothing; its current risks are acceptable.

Let's break down the problem and solve it step by step. Type II Error and Power of the Test:Type II…

Answered: The null hypothesis is rejected when…

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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An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 119 cm and a standard deviation of 5.7 cm. A. Find the probability that one selected subcomponent is longer than 121 cm. Probability = B. Find the probability that if 4 subcomponents are randomly selected, their mean length exceeds 121 cm. Probability = C. Find the probability that if 4 are randomly selected, all 4 have lengths that exceed 121 cm. Probability =
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 6 IQ points of the true mean. Assume that σ=15 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 23 couples. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of girls in groups of 23 births. The value of the mean is µ = (Type an integer or a decimal. Do not round.) The value of the standard deviation is o = (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values of girls or fewer are significantly low. (Round to one decimal place as needed.) Values of girls or greater are significantly high. (Round to one decimal place as needed.) c. Is the result of 19 girls a result that is significantly high? What does it…
An IQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 7 IQ points of the true mean. Assume that σ=14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
The body temperatures of adults have a mean of 98.6° F and a standard deviation of 0.60° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.5° F. Hint: You will need to use the sampling distribution of the sample mean. 0.9360 0.0228 0.8413 0.8188
Provide an original example of some practical case where we can use the normal distribution (e.g., IQ scores follow a normal distribution of probabilities with a mean IQ of 100 and a standard deviation of 15 IQ points.). Assign your numbers for mean 70 and standard deviation 30. Make sure 70 is about four times bigger than 30. Then select any number 90 below or above mean 70, but not too far from 70. Find following two probabilities: 1) P(x < a)2) P(x > a)Use the formula z = (a - μ)/σ to calculate your z-value. Please refer to the Appendix Table for the Standard Normal Distribution Hint: To find P(x>a) use formula: P(x>a) = 1 - P(x<a). Describe how to would find P( 65 < x < 25). Provide an original example to illustrate how to find such probabilities.
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 41 couples. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of girls in groups of 41 births. The value of the mean isu = (Type an integer or a decimal. Do not round.) The value of the standard deviation is o = (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. girls or fewer are significantly low. (Round to one decimal place as needed.) Values of Values of girls or greater are significaly high. (Round to one decimal place as needed.) c. Is the result of 39 girls a result that is significantly high? What does it…
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Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 43 couples. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of girls in groups of 43 births. The value of the mean is = (Type an integer or a decimal. Do not round.) The value of the standard deviation is o = (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values of girls or fewer are significantly low. (Round to one decimal place as needed.) Values of girls or greater are significantly high. (Round to one decimal place as needed.) c. Is the result of 41 girls a result that is significantly high? What does it…
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 44 couples. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of girls in groups of 44 births. The value of the mean is (Type an integer or a decimal. Do not round.) The value of the standard deviation is o = (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values of girls or fewer are significantly low. (Round to one decimal place as needed.) Values of girls or greater are significantly high. (Round to one decimal place as needed.) c. Is the result of 35 girls a result that is significantly high? What does it…
An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 115 cm and a standard deviation of 5.5 cm. A. Find the probability that one selected subcomponent is longer than 117 cm. Probability = B. Find the probability that if 4 subcomponents are randomly selected, their mean length exceeds 117 cm. Probability = C. Find the probability that if 4 are randomly selected, all 4 have lengths that exceed 117 cm. Probability =
Suppose a population with a mean of 100 and a variance of 900 was given. The central limit theorem was applied with a sample size ?? ≥ 25. A random sample of size ?? = 30 wasobtained. Find the: i. mean and variance of sampling distribution for sample means. ii. probability that 96 ≤ ??̅≤ 110. iii. probability that ??̅≤ 107.

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