Question

The average salary for American college graduates is $43,500. You suspect that the average is different for graduates from your college. The 52 randomly selected graduates from your college had an average salary of $39,906 and a standard deviation of $14,280. 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:  ? p μ  ? = > ≠ <    

3. The test statistic ? z t  =  (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 reject fail to reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the populaton mean is significantly different from 43,500 at αα = 0.10, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is different from 43,500.
   • The data suggest that the population mean is not significantly different from 43,500 at αα = 0.10, so there is statistically insignificant evidence to conclude that the population mean salary for graduates from your college is different from 43,500.
   • The data suggest that the sample mean is not significantly different from 43,500 at αα = 0.10, so there is statistically insignificant evidence to conclude that the sample mean salary for graduates from your college is different from 39,906.
8. Interpret the p-value in the context of the study.
   • There is a 7.54150152% chance of a Type I error.
   • If the population mean salary for graduates from your college is $43,500 and if another 52 graduates from your college are surveyed then there would be a 7.54150152% chance that the population mean would either be less than $39,906 or greater than $47,094.
   • If the population mean salary for graduates from your college is $43,500 and if another 52 graduates from your college are surveyed then there would be a 7.54150152% chance that the sample mean for these 52 graduates from your college would either be less than $39,906 or greater than $47,094.
   • There is a 7.54150152% chance that the population mean salary for graduates from your college is not equal to $43,500 .
9. Interpret the level of significance in the context of the study.
   • If the population mean salary for graduates from your college is $43,500 and if another 52 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 different from $43,500.
   • If the population population mean salary for graduates from your college is different from $43,500 and if another 52 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 $43,500.
   • There is a 10% chance that the population mean salary for graduates from your college is different from $43,500.
   • There is a 10% chance that your won't graduate, so what's the point?

Answer 1

Note: There is a slight difference in p-value, please check with your professor and let me know because I have used the correct formula, maybe he used a different tool for that.

a. We should select t test for a population mean b. The null and alternative hypotheses are H 43500 H u43500 c. The test statistic is calculated as: T- 39906-43 500 14280 52 -1.815 The t-value is -1.815 d. The degrees of freedom are 52 1 51 The calculation ofp-value in Excel is: fr T.DIST.2T(ABS(-1.815),51) D E F 0.075407 The p-value is 0.0754

The p-value is less than alpha. That is p-value Sa e. f. Based on this, we should reject the null hypothesis g. Thus, the final conclusion is that The data suggest that the population mean is significantly different from 43,500 at aa= 0.10, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is different from 43,500. h. There is a 7.54150152 % chance that the population mean salary for graduates from your college is not equal to $43,500. If the population mean salary for graduates from your college is $43,500 and if another 52 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 different from $43,500.