Question

The average salary for American college graduates is $48,000. You suspect that the average is different for graduates from your college. The 50 randomly selected graduates from your college had an average salary of $53,352 and a standard deviation of $14,890. What can be concluded at the αα = 0.05 level of significance?

For this study, we should use Select an answer z-test for a population proportion t-test for a population mean

The null and alternative hypotheses would be:

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

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

The test statistic ? t z  =  (please show your answer to 3 decimal places.)

The p-value =  (Please show your answer to 4 decimal places.)

The p-value is ? ≤ >  αα

Based on this, we should Select an answer reject fail to reject accept  the null hypothesis.

Thus, the final conclusion is that ...

The data suggest that the populaton mean is significantly different from 48,000 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is different from 48,000.

The data suggest that the sample mean is not significantly different from 48,000 at αα = 0.05, so there is statistically insignificant evidence to conclude that the sample mean salary for graduates from your college is different from 53,352.

The data suggest that the population mean is not significantly different from 48,000 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean salary for graduates from your college is different from 48,000.

Interpret the p-value in the context of the study.

There is a 1.42541396% chance that the population mean salary for graduates from your college is not equal to $48,000 .

If the population mean salary for graduates from your college is $48,000 and if another 50 graduates from your college are surveyed then there would be a 1.42541396% chance that the population mean would either be less than $42,648 or greater than $53,352.

There is a 1.42541396% chance of a Type I error.

If the population mean salary for graduates from your college is $48,000 and if another 50 graduates from your college are surveyed then there would be a 1.42541396% chance that the sample mean for these 50 graduates from your college would either be less than $42,648 or greater than $53,352.

Interpret the level of significance in the context of the study.

If the population mean salary for graduates from your college is $48,000 and if another 50 graduates from your college are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean salary for graduates from your college is different from $48,000.

There is a 5% chance that your won't graduate, so what's the point?

There is a 5% chance that the population mean salary for graduates from your college is different from $48,000.

If the population population mean salary for graduates from your college is different from $48,000 and if another 50 graduates from your college are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean salary for graduates from your college is equal to $48,000.

Answer 1

Solution :

Given that,

= $53,352

s = $14,890

n = 50

t-test for a population mean

Degrees of freedom = df = n - 1 = 50- 1 = 49

= 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,49 = 2.010

Hypothesis:

H0 :   = $48,000

Ha : ≠ $48,000

Test Statistic:

t = ( - ) / (s /n)

t = (53,352 - 48,000) / ( 14,890/ 50)

t = 2.542

P-value = 0.0142

if P- value ≤ = 0.05 then reject H0.

Reject the Null hypothesis

conclusion:

The data suggest that the populaton mean is significantly different from 48,000 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean salary for graduates from your college is different from 48,000.

If the population mean salary for graduates from your college is $48,000 and if another 50 graduates from your college are surveyed then there would be a 5% chance that we would end up falsely concluding that the population mean salary for graduates from your college is different from $48,000.