Question

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.

Answer 1

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.