A researcher is interested in estimating the mean weight of a semi tracker truck to determine the potential load capacity. She takes a rando

Question

A researcher is interested in estimating the mean weight of a semi tracker truck to determine the potential load capacity. She takes a random sample of 17 trucks and computes a sample mean of 20,000 pounds with sample standard deviation of 1,500. The 95% confidence interval for the population mean weight of a semi tracker truck is____________.

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Claire 2 weeks 2021-10-12T13:15:11+00:00 1 Answer 0

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    2021-10-12T13:16:30+00:00

    Answer:

    (19229.11 ,20770.89)

    Step-by-step explanation:

    We are given the following information:

    Sample size, n = 17

    Sample mean = 20,000 pounds

    Sample standard deviation = 1,500 pounds

    Confidence level = 95%

    Significance level = 5% = 0.05

    95% Confidence interval:  

    \bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}  

    Putting the values, we get,  

    t_{critical}\text{ at degree of freedom 16 and}~\alpha_{0.05} = \pm 2.119  

    20000 \pm 2.119(\displaystyle\frac{1500}{\sqrt{17}} ) = 20000 \pm 770.89 = (19229.11 ,20770.89)  

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