An athletic trainer is concerned that his athletes are not drinking enough water during games.He randomly samples 11 previous games with comparable temperature and humidity and records the amount of water consumed by the team in liters (shown in the table).Conduct a sign test to see if the median amount of water consumed exceeds 30 L.(Assume that the amount of water consumed per game is a continuous variable.)
Amount of Water Consumed per Game (in liters)

Select the correct critical value (CV), test statistic (TS), and decision.(Use α = 0.10.)
A) CV = 7, TS = 3, fail to reject H₀
B) CV = 8, TS = 4, fail to reject H₀
C) CV = 8, TS = 3, fail to reject H₀
D) CV = 7, TS = 4, fail to reject H₀

Question

An athletic trainer is concerned that his athletes are not drinking enough water during games.He randomly samples 11 previous games with comparable temperature and humidity and records the amount of water consumed by the team in liters (shown in the table).Conduct a sign test to see if the median amount of water consumed exceeds 30 L.(Assume that the amount of water consumed per game is a continuous variable.) ​
Amount of Water Consumed per Game (in liters)

Select the correct critical value (CV), test statistic (TS), and decision.(Use α = 0.10.)
A) CV = 7, TS = 3, fail to reject H₀ 
B) CV = 8, TS = 4, fail to reject H₀ 
C) CV = 8, TS = 3, fail to reject H₀ 
D) CV = 7, TS = 4, fail to reject H₀

Quizplus · Accepted Answer

To conduct a sign test: 
1. State the null hypothesis (H₀) and alternative hypothesis (H₁).
2. Determine the level of significance (α) and the critical value (CV).
3. Calculate the test statistic (TS).
4. Make a decision to either reject or fail to reject the null hypothesis.

Step 1: 
H₀: The median amount of water consumed is 30 L.
H₁: The median amount of water consumed is greater than 30 L.

Step 2: 
α = 0.10 (given). 
From the sign test table, the critical value for n = 11 with α = 0.10 is 8.

CV = 8

Step 3: 
To calculate the test statistic, we count the number of times the amount of water consumed was above 30 L. 
We have 8 positive signs and 3 negative signs.

TS = min(8, 3) = 3

Step 4: 
TS = 3 is less than CV = 8. Therefore, we fail to reject the null hypothesis. 
There is not enough evidence to conclude that the median amount of water consumed exceeds 30 L.

An Athletic Trainer Is Concerned That His Athletes Are Not