Question

The average salary in this city is $47,300. Is the average less for single people? 60 randomly selected single people who were surveyed had an average salary of $46,132 and a standard deviation of $10,540. What can be concluded at the αα= 0.05 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:  ? μ p  ? > = ≠ <       

H1:  ? p μ  ? > < = ≠    

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 accept reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the populaton mean is significantly less than 47,300 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean salary for singles is less than 47,300.
   • The data suggest that the sample mean is not significantly less than 47,300 at αα = 0.05, so there is statistically insignificant evidence to conclude that the sample mean salary for singles is less than 46,132.
   • The data suggest that the population mean is not significantly less than 47,300 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean salary for singles is less than 47,300.
8. Interpret the p-value in the context of the study.
   • There is a 19.70389682% chance that the population mean salary for singles is less than $47,300.
   • There is a 19.70389682% chance of a Type I error.
   • If the population mean salary for singles is $47,300 and if another 60 singles are surveyed then there would be a 19.70389682% chance that the sample mean for these 60 singles surveyed would be less than $46,132.
   • If the population mean salary for singles is $47,300 and if another 60 singles are surveyed then there would be a 19.70389682% chance that the population mean salary for singles would be less than $47,300.
9. Interpret the level of significance in the context of the study.
   • There is a 5% chance that the population mean salary for singles is less than $47,300.
   • There is a 5% chance that you won the lottery, so you may not have to even have to worry about passing this class.
   • If the population population mean salary for singles is less than $47,300 and if another 60 singles are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean salary for singles is equal to $47,300.
   • If the population mean salary for singles is $47,300 and if another 60 singles are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean salary for singles is less than $47,300.

Answer 1

• The data suggest that the population mean is notsignificantly less than 47,300 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean salary for singles is less than 47,300.

• There is a 19.70389682% chance that the population mean salary for singles is less than $47,300.
• There is a 5% chance that the population mean salary for singles is less than $47,300.