A Company Hopes to Improve Its Engines, Setting a Goal $3 \%$

question 13

Multiple Choice

A company hopes to improve its engines, setting a goal of no more than $3 \%$ of customers using their warranty on defective engine parts. A random survey of 1400 customers found only 30 with complaints. Create a $95 \%$ confidence interval for the true level of warranty users among all customers.

• A) Based on the data, we are \(95 \%\) confident the proportion of warranty users is between \(2.0 \%\) and \(2.9 \%\). Therefore, the company has met its goal.
• B) Based on the data, we are \(95 \%\) confident the proportion of warranty users is between \(1.4 \%\) and \(2.9 \%\). Therefore, the company has met its goal.
• C) Based on the data, we are \(95 \%\) confident the proportion of warranty users is between \(1.4 \%\) and \(3.8 \%\). Therefore, the company has not met its goal.
• D) Based on the data, we are \(95 \%\) confident the proportion of warranty users is between \(1 \%\) and \(3 \%\). Therefore, the company has met its goal.
• E) Based on the data, we are \(95 \%\) confident the proportion of warranty users is between \(0 \%\) and \(2.9 \%\). Therefore, the company has met its goal.

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Definitions:

Groups

Collections of individuals who interact with one another, share similar characteristics, and collectively have a sense of unity or identity.

Competitive Situations

Scenarios in which individuals or groups compete against each other to achieve a specific goal or outcome.

Neuroticism

A personality trait characterized by emotional instability, anxiety, moodiness, worry, and a tendency towards negative emotions.

Negative Affectivity

A characteristic of personality marked by a consistent tendency toward negative feelings and a low self-esteem.