Question

On average, Americans have lived in 3 places by the time they are 18 years old. Is this average less for college students? The 69 randomly selected college students who answered the survey question had lived in an average of 2.83 places by the time they were 18 years old. The standard deviation for the survey group was 1. What can be concluded at the α = 0.10 level of significance?

A) For this study, we should use (Z-Test for population proportion or T-Test for population mean)

B) The null and alternative hypotheses would be:

H 0 : (?,P,μ) (?,<,>,=,≠) Answer:__________

H 1 : (?,P,μ) (?,<,>,=,≠) Answer:__________

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

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

E) The p-value is α (?, ≥,≤ ).

F) Based on this, we should the null hypothesis. (Reject,Fail to Reject, or Accept)

G) Thus, the final conclusion is that ...

Mark an X on the correct answer for each question below

____The data suggest that the sample mean is not significantly less than 3 at α = 0.10, so there is statistically insignificant evidence to conclude that the sample mean number of places that college students lived in by the time they were 18 years old is less than 2.83.

_____The data suggest that the populaton mean is significantly less than 3 at α = 0.10, so there is statistically significant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is less than 3.

____The data suggest that the population mean is not significantly less than 3 at α = 0.10, so there is statistically insignificant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is less than 3.

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

____There is a 8.12364684% chance that the population mean number of places that college students lived in by the time they were 18 years old is less than 3.

____If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 69 college students, then there would be a 8.12364684% chance that the population mean number of places that college students lived in by the time they were 18 years old would be less than 3.

____There is a 8.12364684% chance of a Type I error.

____If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 69 college students, then there would be a 8.12364684% chance that the sample mean for these 69 college students would be less than 2.83.

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

____If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 69 college students, then there would be a 10% chance that we would end up falsely concluding that the population mean number of places that college students lived in by the time they were 18 years old is less than 3.

____If the population mean number of places that college students lived in by the time they were 18 years old is less than 3 and if you survey another 69 college students, then there would be a 10% chance that we would end up falsely concluding that the population mean number of places that college students lived in by the time they were 18 years old is equal to 3.

____There is a 10% chance that the population mean number of places that college students lived in by the time they were 18 years old is less than 3.

____There is a 10% chance that none of this is real since you have been hooked up to virtual reality since you were born.

Answer 1

A)

T-Test for population mean

B-F)

G)

The data suggest that the populaton mean is significantly less than 3 at α = 0.10, so there is statistically significant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is less than 3.

H)

There is a 8.12364684% chance of a Type I error.

____If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 69 college students, then there would be a 8.12364684% chance that the sample mean for these 69 college students would be less than 2.83.

I)

If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 69 college students, then there would be a 10% chance that we would end up falsely concluding that the population mean number of places that college students lived in by the time they were 18 years old is less than 3.