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Answer :
Answer:
The reason that 0.35 should not be used to estimate the population proportion of the 30,000 new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven is that 0.35 does not represent the sample proportion.
The correct sample proportion is 0.14 (140/1,000) and not 0.35 (140/400). It is this that can be used to estimate the population proportion and not 0.35.
Step-by-step explanation:
a) Data and Calculations:
New cars sold by the automobile manufacturer = 30,000
Number of customers that the 30,000 new cars were sold to = 30,000
Simple random sample = 1,000 customers
Number of customers from the SRS that reported a problem = 400
This is equal to 40% of the sample (400/1,000 * 100)
Proportion of customers who reported a problem (specifically) with the power door locks = 140/400 = 0.35
Proportion of customers out of the sample that reported specifically a problem with the power door locks = 140/1000 = 0.14.
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Rewritten by : Barada
To understand why 0.35 should not be used to estimate the population proportion of the 30,000 new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven, we need to analyze the information given and how sampling works.
Clarification of Proportions: The number 0.35 represents the proportion of the total 1,000 sampled cars that experienced any mechanical problem. This means 35% of the sampled cars had issues in general, but it does not specifically address problems just with the power door locks.
Specific Issues vs. General Problems: Among the 400 customers who reported any mechanical problems, only 140 reported issues specifically with the power door locks. Therefore, the percentage of problems specifically with the power door locks is not based on the entire sample of 1,000, but rather on the subset of 400.
Correct Calculation for Specific Issue:
- Total sampled cars: 1,000
- Customers with any problem: 400 (40% of 1,000)
- Customers with door lock problems: 140 (32.5% of 400)
To find out the proportion of cars with power door lock issues out of the total sampled, we use:
[tex]\text{Proportion of door lock problems} = \frac{140}{1000} = 0.14[/tex]
This tells us that only 14% of the total sampled cars had power door lock problems.
Conclusion: This distinction is crucial because using 0.35 would incorrectly inflate the proportion of cars with power door lock problems when we're actually interested in those specific issues across the entire population. The accurate estimate for cars having power door lock issues should reflect the ratio of those issues out of the entire sample of customers, which is 0.14, or 14%.
