erage American consumes 84 liters of alcohol per year. Does the average college student consume less alcohol per year? A researcher surveyed 14 randomly selected college students and found that they averaged 74.4 liters of alcohol consum

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Topic Video
Question

The average American consumes 84 liters of alcohol per year. Does the average college student consume less alcohol per year? A researcher surveyed 14 randomly selected college students and found that they averaged 74.4 liters of alcohol consumed per year with a standard deviation of 21 liters. What can be concluded at the the αα = 0.01 level of significance?

 H0:

 H1:

The test statistic:

The p-value = 

he p-value is ? a

  1. Based on this, we should Select an answer accept fail to reject reject  the null hypothesis.
  2. Thus, the final conclusion is that ...
    • The data suggest the populaton mean is significantly less than 84 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean amount of alcohol consumed by college students is less than 84 liters per year.
    • The data suggest that the population mean amount of alcohol consumed by college students is not significantly less than 84 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 less than 84 liters per year.
    • The data suggest the population mean is not significantly less than 84 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 84 liters per year.
Expert Solution
Step 1

The  null and alternative hypotheses are:

Ho: \mu = 84

H1: \mu < 84

This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation, will be used.

The t-statistic is computed as follows:

Probability homework question answer, step 1, image 1

The p-value with 13(n-1) degrees of freedom and left tailed test is , and since , it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean  is less than 84, at the 0.01 significance level.

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON