A hypothesis test is conducted to test whether the mean age of clients at a certain health spa is equal to 25 or not. It is known that the population standard deviation of clients at the spa is 10 years. 36 clients are randomly selected, and their ages recorded, with the sample mean age being 22.8 years. What is your decision, at the 5% level of significance, regarding the null hypothesis that the mean age is equal to 25? A.reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is less than 25 B.reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is not equal to 25 C.reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is more than 25 D.do not reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is 25 E.do not reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is less than 25Please explain. Thank you.

Name: A hypothesis test is conducted to test whether the mean age of clients
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Description: A hypothesis test is conducted to test whether the mean age of clients at a certain health spa is equal to 25 or not. It is known that the population standard deviation of clients at the spa is 10 years. 36 clients are randomly selected, and their ag

Let, μ denote the population mean σ denote the population standard deviationn denote the…

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MATLAB: An Introduction with Applications

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Author:Amos Gilat

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A hypothesis test is conducted to test whether the mean age of clients at a certain health spa is equal to 25 or not. It is known that the population standard deviation of clients at the spa is 10 years. 36 clients are randomly selected, and their ages recorded, with the sample mean age being 22.8 years.

What is your decision, at the 5% level of significance, regarding the null hypothesis that the mean age is equal to 25?

	A.	reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is less than 25
	B.	reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is not equal to 25
	C.	reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is more than 25
	D.	do not reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is 25
	E.	do not reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is less than 25

Please explain. Thank you.

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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