The average salary for American college graduates is $48,200. You suspect that the average is less for graduates from your college. The 51 randomly selected graduates from your college had an average salary of $46,917 and a standard deviation of $17,450. What can be concluded at the αα = 0.05 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: ? μ p 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 ? > ≤ ααBased on this, we should Select an answer fail to reject accept reject the null hypothesis.Thus, the final conclusion is that ...The data suggest that the sample mean is not significantly less than 48,200 at αα = 0.05, so there is statistically insignificant evidence to conclude that the sample mean salary for graduates from your college is less than 46,917.The data suggest that the population mean is not significantly less than 48,200 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean salary for graduates from your college is less than 48,200.The data suggest that the populaton mean is significantly less than 48,200 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is less than 48,200.Interpret the p-value in the context of the study.If the population mean salary for graduates from your college is $48,200 and if another 51 graduates from your college are surveyed then there would be a 30.09279614% chance that the population mean salary for graduates from your college would be less than $48,200.If the population mean salary for graduates from your college is $48,200 and if another 51 graduates from your college are surveyed then there would be a 30.09279614% chance that the sample mean for these 51 graduates from your college would be less than $46,917.There is a 30.09279614% chance that the population mean salary for graduates from your college is less than $48,200. There is a 30.09279614% chance of a Type I error.Interpret the level of significance in the context of the study.There is a 5% chance that the population mean salary for graduates from your college is less than $48,200.If the population mean salary for graduates from your college is $48,200 and if another 51 graduates from your college are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean salary for graduates from your college is less than $48,200.There is a 5% chance that your won't graduate, so what's the point?If the population population mean salary for graduates from your college is less than $48,200 and if another 51 graduates from your college are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean salary for graduates from your college is equal to $48,200.

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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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The average salary for American college graduates is $48,200. You suspect that the average is less for graduates from your college. The 51 randomly selected graduates from your college had an average salary of $46,917 and a standard deviation of $17,450. What can be concluded at the αα = 0.05 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: ? μ p 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 that the sample mean is not significantly less than 48,200 at αα = 0.05, so there is statistically insignificant evidence to conclude that the sample mean salary for graduates from your college is less than 46,917.
- The data suggest that the population mean is not significantly less than 48,200 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean salary for graduates from your college is less than 48,200.
- The data suggest that the populaton mean is significantly less than 48,200 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is less than 48,200.
Interpret the p-value in the context of the study.
- If the population mean salary for graduates from your college is $48,200 and if another 51 graduates from your college are surveyed then there would be a 30.09279614% chance that the population mean salary for graduates from your college would be less than $48,200.
- If the population mean salary for graduates from your college is $48,200 and if another 51 graduates from your college are surveyed then there would be a 30.09279614% chance that the sample mean for these 51 graduates from your college would be less than $46,917.
- There is a 30.09279614% chance that the population mean salary for graduates from your college is less than $48,200.
- There is a 30.09279614% chance of a Type I error.
Interpret the level of significance in the context of the study.
- There is a 5% chance that the population mean salary for graduates from your college is less than $48,200.
- If the population mean salary for graduates from your college is $48,200 and if another 51 graduates from your college are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean salary for graduates from your college is less than $48,200.
- There is a 5% chance that your won't graduate, so what's the point?
- If the population population mean salary for graduates from your college is less than $48,200 and if another 51 graduates from your college are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean salary for graduates from your college is equal to $48,200.

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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