Question

If the population standard deviation of the stopping distance is provided as σ = 6.7 feet. Estimate the average stopping distance of all Model A tires with a 94% confidence interval.

Answer 1

Complete Question

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Answer:

The estimate of the average stopping distance of all model A tires with a 94% confidence interval is

`132.94 <  \mu < 144.86`

Explanation:

From the question we see that

The sample size is n = 8

The population standard deviation is
`\sigma = 6.7`

Generally the sample mean is mathematically represented as

`\= x = (\sum x_i )/(n)`

=>
`\= x = ( 145 + 152 + \cdots + 133)/(8)`

=>
`\= x = 138.9`

From the question we are told the confidence level is 95% , hence the level of significance is

`\alpha = (100 - 94 ) \%`

=>
`\alpha = 0.04`

Generally the degree of freedom is mathematically represented as

`df = n - 1`

=>
`df = 8 - 1`

=>
`df = 7`

Because the n < 30 we will making use of the t table

Generally from the t distribution table the critical value of
`(\alpha )/(2)` at a degree of freedom of
`df = 7` is

`t_{(\alpha )/(2), 7 } = 2.517`

Generally the margin of error is mathematically represented as

`E = t_{(\alpha )/(2) , df} *  (\sigma )/(√(n) )`

=>
`E = 2.517 *  (6.7 )/(√(8) )`

=>
`E =5.96`

Generally 94% confidence interval is mathematically represented as

`\= x -E <  \mu <  \=x  +E`

=>
`138.9  -5.96 <  \mu < 138.9  + 5.96`

=>
`132.94 <  \mu < 144.86`