for option (d) first blank options are: a decrease/an increase. second blank options are: sample mean/critical value/sample size/standard deviation, third blank options are: decrease/not change/increase A random sample of 100 observations from a normally distributed population possesses a mean equal to 92.7 and a standard deviation equal to 5.9. Use this information to complete parts a through e below.a. Find a 95% confidence interval for µ.(Round to two decimal places as needed.)b. What do you mean when you say that a confidence coefficient is 0.95?O A. A confidence coefficient of 0.95 means that there is a probability of 0.95 that an interval estimator constructed using this coefficient will enclose the population parameter.B. A confidence coefficient of 0.95 means that there is a probability of 0.95 that an interval estimator constructed using this coefficient will contain all of the values in the relevant sample.O C. A confidence coefficient of 0.95 means that 95% of the values in the population will be contained in an interval estimator constructed using this coefficient.D. A confidence coefficient of 0.95 means that 95% of the values in any sample taken from the population will be contained in an interval estimator constructed using this coefficient.c. Find a 99% confidence interval for µ.(Round to two decimal places as needed.)d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?Increasing the confidence coefficient while keeping the sample size fixed will causein theThis means that the width of the confidence interval wille. Would your confidence intervals of parts a and c be valid if the distribution of the original population were not normal? Explain.O A. Yes, since the sample sizes are large (n > 30), the condition guarantees that the sampling distribution of x is approximately normal.B. Yes, since the sample was randomly selected from the target population, the sampling distribution of x is guaranteed to be approximately normal.C. No, the underlying distribution must be normal for the validity of these confidence intervalsD. Yes, since the confidence level is at least 90%, the underlying distribution need not be normal.O E. Yes, since the sample sizes are large (n2 30) and randomly selected from the target population, the condition guarantees that the sampling distribution of x is approximately normal.

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved. a)At 95% confidence level, the value of z is 1.96. Then, the confidence interval isx±zsn=92.7±1.965.9100=92.7±1.965.910=92.7±1.960.59=92.7±1.16=91.54 , 93.86b)The option A is correct.c) At 99% confidence level, the value of z is 2.58. Then, the confidence interval isx±zsn=92.7±2.585.9100=92.7±2.585.910=92.7±2.580.59=92.7±1.52=91.18 , 94.22

Answered: A random sample of 100 observations…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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for option (d) first blank options are: a decrease/an increase. second blank options are: sample mean/critical value/sample size/standard deviation, third blank options are: decrease/not change/increase

A random sample of 100 observations from a normally distributed population possesses a mean equal to 92.7 and a standard deviation equal to 5.9. Use this information to complete parts a through e below.
a. Find a 95% confidence interval for µ.
(Round to two decimal places as needed.)
b. What do you mean when you say that a confidence coefficient is 0.95?
O A. A confidence coefficient of 0.95 means that there is a probability of 0.95 that an interval estimator constructed using this coefficient will enclose the population parameter.
B. A confidence coefficient of 0.95 means that there is a probability of 0.95 that an interval estimator constructed using this coefficient will contain all of the values in the relevant sample.
O C. A confidence coefficient of 0.95 means that 95% of the values in the population will be contained in an interval estimator constructed using this coefficient.
D. A confidence coefficient of 0.95 means that 95% of the values in any sample taken from the population will be contained in an interval estimator constructed using this coefficient.
c. Find a 99% confidence interval for µ.
(Round to two decimal places as needed.)
d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?
Increasing the confidence coefficient while keeping the sample size fixed will cause
in the
This means that the width of the confidence interval will
e. Would your confidence intervals of parts a and c be valid if the distribution of the original population were not normal? Explain.
O A. Yes, since the sample sizes are large (n > 30), the condition guarantees that the sampling distribution of x is approximately normal.
B. Yes, since the sample was randomly selected from the target population, the sampling distribution of x is guaranteed to be approximately normal.
C. No, the underlying distribution must be normal for the validity of these confidence intervals
D. Yes, since the confidence level is at least 90%, the underlying distribution need not be normal.
O E. Yes, since the sample sizes are large (n2 30) and randomly selected from the target population, the condition guarantees that the sampling distribution of x is approximately normal.

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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