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True or False: A race car driver tested his car for time from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 mean time is 4.52 seconds to 5.18 seconds.

User Diogojme
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1 Answer

3 votes

Answer:

The given statement is false.

Explanation:

We are given the following in the question:

95% confidence interval: (4.53,5.18)

Sample mean,
\bar{x} = 4.85 seconds

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, σ = 1.47 seconds

Degree of freedom = n - 1 = 19

95% Confidence interval:


\bar{x} \pm t_(critical)\displaystyle(s)/(√(n))

Putting the values, we get,


t_(critical)\text{ at degree of freedom 4 and}~\alpha_(0.01) = \pm 2.09


4.85 \pm 2.09(( 1.47)/(√(20)) )\\\\ = 4.85 \pm 0.69 \\\\= (4.16 ,5.54)

Thus, the calculated confidence interval is different from the given confidence interval.

Hence, the given statement is false.

User Chatpitau
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