Question

The average salary for American college graduates is $42,900. You suspect that the average is less for graduates from your college. The 49 randomly selected graduates from your college had an average salary of $38,173 and a standard deviation of $10,190. What can be concluded at the αα = 0.01 level of significance?

1. For this study, we should use Select an answert-test for a population meanz-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0:   ?pμ ?=≠><   

H1:H1:   ?pμ ?><≠=

3. The test statistic ?tz = (please show your answer to 3 decimal places.)
4. The p-value = (Please show your answer to 4 decimal places.)
5. The p-value is ?>≤ αα
6. Based on this, we should Select an answeracceptfail to rejectreject the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the populaton mean is significantly less than 42,900 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is less than 42,900.
   • The data suggest that the population mean is not significantly less than 42,900 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean salary for graduates from your college is less than 42,900.
   • The data suggest that the sample mean is not significantly less than 42,900 at αα = 0.01, so there is statistically insignificant evidence to conclude that the sample mean salary for graduates from your college is less than 38,173.
8. Interpret the p-value in the context of the study.
   • If the population mean salary for graduates from your college is $42,900 and if another 49 graduates from your college are surveyed then there would be a 0.10651237% chance that the population mean salary for graduates from your college would be less than $42,900.
   • There is a 0.10651237% chance that the population mean salary for graduates from your college is less than $42,900.
   • If the population mean salary for graduates from your college is $42,900 and if another 49 graduates from your college are surveyed then there would be a 0.10651237% chance that the sample mean for these 49 graduates from your college would be less than $38,173.
   • There is a 0.10651237% chance of a Type I error.
9. Interpret the level of significance in the context of the study.
   • There is a 1% chance that your won't graduate, so what's the point?
   • There is a 1% chance that the population mean salary for graduates from your college is less than $42,900.
   • If the population mean salary for graduates from your college is $42,900 and if another 49 graduates from your college are surveyed then there would be a 1% chance that we would end up falsely concluding that the population mean salary for graduates from your college is less than $42,900.
   • If the population population mean salary for graduates from your college is less than $42,900 and if another 49 graduates from your college are surveyed then there would be a 1% chance that we would end up falsely concluding that the population mean salary for graduates from your college is equal to $42,900.

Answer 1

Let denotes the average salary in the college.

e) The p-value is < α

f) reject the null hypothesis.

g) The data suggest that the population mean is significantly less than 42,900 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is less than 42,900.

h) If the population mean salary for graduates from your college is $42,900 and if another 49 graduates from your college are surveyed then there would be a 0.10651237% chance that the sample mean for these 49 graduates from your college would be less than $38,173.

i) If the population mean salary for graduates from your college is $42,900 and if another 49 graduates from your college are surveyed then there would be a 1% chance that we would end up falsely concluding that the population mean salary for graduates from your college is less than $42,900.