Question

The average salary in this city is $42,400. Is the average more for single people? 46 randomly selected single people who were surveyed had an average salary of $42,907 and a standard deviation of $11,240. What can be concluded at the αα = 0.01 level of significance?

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

H0:H0:  ? p μ  Select an answer = ≤ ≥ < > ≠       

H1:H1:  ? p μ  Select an answer ≤ ≠ ≥ = < >    

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 accept fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean is not significantly greater than 42,400 at αα = 0.01, so there is not enough evidence to conclude that the population mean salary for singles is greater than 42,400.
   • The data suggest that the sample mean is not significantly greater than 42,400 at αα = 0.01, so there is not enough evidence to conclude that the sample mean salary for singles is greater than 42,907.
   • The data suggest that the populaton mean is significantly greater than 42,400 at αα = 0.01, so there is enough evidence to conclude that the population mean salary for singles is greater than 42,400.
8. Interpret the p-value in the context of the study.
   • There is a 38.04891721% chance of a Type I error.
   • If the population mean salary for singles is $42,400 and if another 46 singles are surveyed then there would be a 38.04891721% chance that the population mean salary for singles would be greater than $42,400.
   • There is a 38.04891721% chance that the population mean salary for singles is greater than $42,400 .
   • If the population mean salary for singles is $42,400 and if another 46 singles are surveyed then there would be a 38.04891721% chance that the sample mean for these 46 singles surveyed would be greater than $42,907.
9. Interpret the level of significance in the context of the study.
   • There is a 1% chance that the population mean salary for singles is greater than $42,400.
   • If the population population mean salary for singles is greater than $42,400 and if another 46 singles are surveyed then there would be a 1% chance that we would end up falsely concluding that the population mean salary for singles is equal to $42,400.
   • There is a 1% chance that you won the lottery, so you may not have to even have to worry about passing this class.
   • If the population mean salary for singles is $42,400 and if another 46 singles are surveyed then there would be a 1% chance that we would end up falsely concluding that the population mean salary for singles is greater than $42,400.

Answer 1

f) P values are frequently misinterpreted. A common mistake is the notion that they represent the likelihood of rejecting a null hypothesis that is actually true (Type 1 error), so there is a 38.0489% of type 1 erroe.

g) there is 1% chance thet the population mean salary for singles is greater than 42400$.