A population is distributed with a known standard deviation, σ = 15 units. A random sample of size 50 is obtained from this population. The mean of this sample is 80. True or False: Since the sample size is greater than 25 the distribution of sample means from this population should be approximately normally distributed. 2. What is the lower limit of the 95% confidence interval for the population mean μ? (2 dp) distributed. 3. What is the upper limit of the 95% confidence interval for the population mean μ? (2 dp)4. Based on your confidence interval, would you believe that the true mean of this population could be 85?

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Description: A population is distributed with a known standard deviation, σ = 15 units. A random sample of size 50 is obtained from this population. The mean of this sample is 80. True or False: Since the sample size is greater than 25 the distribution of sampl

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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A population is distributed with a known standard deviation, σ = 15 units. A random sample of size 50 is obtained from this population. The mean of this sample is 80.

True or False: Since the sample size is greater than 25 the distribution of sample means from this population should be approximately normally distributed.

2. What is the lower limit of the 95% confidence interval for the population mean μ? (2 dp) distributed.

3. What is the upper limit of the 95% confidence interval for the population mean μ? (2 dp)

4. Based on your confidence interval, would you believe that the true mean of this population could be 85?

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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Step 1

As per our guidelines, we are allowed to answer first three sub-parts . Thanks

1) We know that if the sample size is greater than 30 , according to Central limit theorem , the distribution can be approximated using normal distribution

Here n = 50

"True"

σ = 15 units

The mean of this sample , $\bar{x}$ = 80

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