A Hypothesis Test Is to Be Performed $8.4$ Minutes the Manager Has Installed a New Computer System and Possible

question 211

Multiple Choice

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the givensituation.
-Last month the average waiting time at a bank was $8.4$ minutes. The manager has installed a new computer system and claims that people will no longer have to wait as long.
The hypotheses are as follows:
Null hypothesis: average waiting time $= 8.4$ minutes
Alternative hypothesis: average waiting time $< 8.4$ minutes

• A) Rejecting the null hypothesis means there is evidence that the mean waiting time is less than \(8.4\) minutes.
• Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean waiting time is less than \(8.4\) minutes.
• B) Rejecting the null hypothesis means there is evidence that the mean waiting time is not equal to \(8.4\) minutes.
• Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean waiting time is less than \(8.4\) minutes.
• C) Rejecting the null hypothesis means there is insufficient evidence that the mean waiting time is equal to \(8.4\) minutes.
• Accepting the null hypothesis means there is evidence to conclude that the mean waiting time is equal to \(8.4\) minutes.
• D) Rejecting the null hypothesis means there is evidence that the mean waiting time is less than \(8.4\) minutes.
• Accepting the null hypothesis means there is evidence to conclude that the mean waiting time is equal to \(8.4\) minutes.

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Definitions:

Formula

A mathematical expression that defines a relationship among variables.

Cramér's V

An indicator of the relationship strength between two categorical variables, ranging from 0 to 1.

Cramér's V

A measure of association between two nominal variables, giving a value between 0 and 1, where 0 means no association and 1 indicates perfect association.

Expected Frequency

The theoretical frequency of an event occurring in a set of trials, calculated based on probability theory.