Question

The average American consumes 80 liters of alcohol per year. Does the average college student consume more alcohol per year? A researcher surveyed 12 randomly selected college students and found that they averaged 97.6 liters of alcohol consumed per year with a standard deviation of 23 liters. What can be concluded at the the αα = 0.01 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:  ? μ p  Select an answer ≠ = > <       

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

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 reject accept fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean amount of alcohol consumed by college students is not significantly more than 80 liters per year at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is more than 80 liters per year.
   • The data suggest the population mean is not significantly more than 80 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is equal to 80 liters per year.
   • The data suggest the populaton mean is significantly more than 80 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean amount of alcohol consumed by college students is more than 80 liters per year.

Answer 1

Claim : the average college student consume alcohol more than 80 liters per year

Population standard deviation σ is unknown therefore we use t statistic.

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

b) The null and alternative hypotheses would be:

: µ = 80 vs : µ > 80

a) Test statistic : Given : = 97.6, s = 23 , n = 12

t =

=

t = 2.651

b) P value : We can use excel function =TDIST( |t| ,df , tail ) to find the P value

| t | is positive value of test statistic t, df = n-1 and tail =1 for one tail and 2 for two tail

=TDIST(2.651,11,1 )

P value = 0.0113

Given : α = 0.01

c) The p-value is > α

d) Based on this, we should fail to reject the null hypothesis.

e)Thus, the final conclusion is that
The data suggest that the population mean amount of alcohol consumed by college students is not significantly more than 80 liters per year at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is more than 80 liters per year.