The average retirement age in America is 62 years old. Do small business owners retire at a different average age? The data below shows the results of a survey of small business owners who have recently retired. Assume that the distribution of the population is normal. 54, 61, 68, 71, 71, 58, 70, 70, 67, 70, 61, 67 What can be concluded at the the αα = 0.01 level of significance level of significance? For this study, we should use Select an answer t-test for a population mean z-test for a population proportion The null and alternative hypotheses would be: H0:H0: ? p μ Select an answer = > ≠ < H1:H1: ? μ p Select an answer ≠ = > < The test statistic ? z t = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? ≤ > αα Based on this, we should Select an answer fail to reject accept reject the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean retirement age for small business owners is not significantly different from 62 at αα = 0.01, so there is insufficient evidence to conclude that the population mean retirement age for small business owners is different from 62. The data suggest the population mean is not significantly different from 62 at αα = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is equal to 62. The data suggest the populaton mean is significantly different from 62 at αα = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is different from 62.

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Description: The average retirement age in America is 62 years old. Do small business owners retire at a different average age? The data below shows the results of a survey of small business owners who have recently retired. Assume that the distribution of the po

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The average retirement age in America is 62 years old. Do small business owners retire at a different average age? The data below shows the results of a survey of small business owners who have recently retired. Assume that the distribution of the population is normal.

54, 61, 68, 71, 71, 58, 70, 70, 67, 70, 61, 67

What can be concluded at the the αα = 0.01 level of significance level of significance?

For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
The null and alternative hypotheses would be:

H0:H0: ? p μ Select an answer = > ≠ <

H1:H1: ? μ p Select an answer ≠ = > <

The test statistic ? z t = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is ? ≤ > αα
Based on this, we should Select an answer fail to reject accept reject the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the population mean retirement age for small business owners is not significantly different from 62 at αα = 0.01, so there is insufficient evidence to conclude that the population mean retirement age for small business owners is different from 62.
- The data suggest the population mean is not significantly different from 62 at αα = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is equal to 62.
- The data suggest the populaton mean is significantly different from 62 at αα = 0.01, so there is sufficient evidence to conclude that the population mean retirement age for small business owners is different from 62.

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 + ...

Expert Solution

Step 1

Given information-

Population mean, μ = 62 years

Sample size, n = 12

I have used following functions for mean and standard deviation.

=AVERAGE(54:67)

And standard deviation-

=STDEV.S(54:67)

Therefore,

Sample mean, x-bar = 65.67

Sample standard deviation, s = 5.7261

We have to test the claim that the small business owners retire at a different average age.

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