Researchers Have Claimed That the Average Number of Headaches Per $n = 16$

question 6

Multiple Choice

Researchers have claimed that the average number of headaches per student during a semester of Statistics is 11. Statistics students believe the average is higher. In a sample of $n = 16$ students the mean is 12 headaches with a deviation of 2.4. Which of the following represent the null and alternative hypotheses necessary to test the students' belief?

• A) \(H _ { 0 } : \mu = 11\) vs. \(H _ { \mathrm { a } } : \mu > 11\)
• B) \(H _ { 0 } : \mu = 11\) vs. \(H _ { \mathrm { a } } : \mu \neq 11\)
• C) \(H _ { 0 } : \mu < 11\) vs. \(H _ { \mathrm { a } } : \mu = 11\)
• D) \(H _ { 0 } : \mu = 11\) vs. \(H _ { \mathrm { a } } : \mu < 11\)

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Definitions:

Sample Proportion

The fraction or percentage of the sample that possesses a certain property or characteristic.

Probability

An indicator of the probability or risk that a certain event will happen, represented by a numerical value ranging from 0 to 1.

Population Mean

The average of a set of numerical values, calculated by summing all the observations and dividing by the total number of observations in the population.

Finite Population

A population set that contains a countable number of elements or observations.