Question

The average salary for American college graduates is $42,400. You suspect that the average is less for graduates from your college. The 59 randomly selected graduates from your college had an average salary of $41,616 and a standard deviation of $8,550. What can be concluded at the αα = 0.10 level of significance?

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

H0:H0:  ? p μ  ? = ≠ > <       

H1:H1:  ? μ p  ? = > < ≠    

3. The test statistic ? t z  =  (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 answer fail to reject reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the populaton mean is significantly less than 42,400 at αα = 0.10, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is less than 42,400.
   • The data suggest that the sample mean is not significantly less than 42,400 at αα = 0.10, so there is statistically insignificant evidence to conclude that the sample mean salary for graduates from your college is less than 41,616.
   • The data suggest that the population mean is not significantly less than 42,400 at αα = 0.10, so there is statistically insignificant evidence to conclude that the population mean salary for graduates from your college is less than 42,400.
8. Interpret the p-value in the context of the study.
   • There is a 24.20507762% chance that the population mean salary for graduates from your college is less than $42,400.
   • If the population mean salary for graduates from your college is $42,400 and if another 59 graduates from your college are surveyed then there would be a 24.20507762% chance that the sample mean for these 59 graduates from your college would be less than $41,616.
   • If the population mean salary for graduates from your college is $42,400 and if another 59 graduates from your college are surveyed then there would be a 24.20507762% chance that the population mean salary for graduates from your college would be less than $42,400.
   • There is a 24.20507762% chance of a Type I error.
9. Interpret the level of significance in the context of the study.
   • If the population mean salary for graduates from your college is $42,400 and if another 59 graduates from your college are surveyed then there would be a 10% chance that we would end up falsely concluding that the population mean salary for graduates from your college is less than $42,400.
   • If the population population mean salary for graduates from your college is less than $42,400 and if another 59 graduates from your college are surveyed then there would be a 10% chance that we would end up falsely concluding that the population mean salary for graduates from your college is equal to $42,400.
   • There is a 10% chance that your won't graduate, so what's the point?
   • There is a 10% chance that the population mean salary for graduates from your college is less than $42,400.

Answer 1