Pregunta
- A tyre manufacturer wishes to investigate the tread
life of its tyres. A sample of 10 tyres driven 50,000
miles revealed a sample mean of 0.32 inch of
tread remaining with a standard deviation of 0.09
inch. Construct a
population mean. Would it be reasonable for the
manufacturer to conclude that after 50,000 miles
the population mean amount of tread remaining is
0.30 inch?
life of its tyres. A sample of 10 tyres driven 50,000
miles revealed a sample mean of 0.32 inch of
tread remaining with a standard deviation of 0.09
inch. Construct a
population mean. Would it be reasonable for the
manufacturer to conclude that after 50,000 miles
the population mean amount of tread remaining is
0.30 inch?
Ask by Ayala Grant. in Jamaica
Mar 21,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The
Solución
To construct a
where:
-
is the sample mean -
is the critical value from the standard normal distribution for a confidence level -
is the sample standard deviation -
is the sample size
Given:
- Sample mean (
) = 0.32 inch - Sample standard deviation (
) = 0.09 inch - Sample size (
) = 10
First, we need to find the critical value
Now, we can calculate the confidence interval using the formula above.
The
The
To determine if it would be reasonable for the manufacturer to conclude that after 50,000 miles the population mean amount of tread remaining is 0.30 inch, we need to check if the value 0.30 inch falls within the confidence interval.
Since 0.30 inch is within the confidence interval, it would be reasonable for the manufacturer to conclude that after 50,000 miles the population mean amount of tread remaining is 0.30 inch.
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Simplifique esta solución Bonus Knowledge
To construct a
where
Calculating the margin of error:
Thus, the confidence interval is:
Given this interval, it does include
Ever wondered how manufacturers conduct their tests? They often use rigorous protocols and statistical analyses to determine the durability and safety of products. By understanding the average wear and tear, they can design better products that meet safety standards while providing consumers with reliable information on usage.
In real-world applications, this kind of statistical analysis doesn’t just stop with tyres. Think about how it applies to everything from clinical trials for new medicines to understanding consumer Preferences. Companies use confidence intervals to gauge whether their products meet expectations, creating a more informed decision-making process that benefits both the manufacturer and the consumer.
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