Question

a consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.8 seconds. a random sample of 21 sedans has a mean minimum time to travel a quarter mile of 15.6 seconds and a standard deviation of 2.12 seconds. at α = 0.05 is there enough evidence to support the consumer groups claim? complete parts (a) through (d) below. assume the population is normally distributed. (a) identify the claim and state ( h_0 ) and ( h_a ). ( h_0: mu leq 14.8 ) ( h_a: mu > 14.8 ) (type integers or decimals. do not round.) the claim is the alternative hypothesis (b) use technology to find the p - value. find the standardized test statistic, t. ( t = 1.81 ) (round to two decimal places as needed) obtain the p - value. ( p = 0.042 ) (round to three decimal places as needed)

Explanation:

Step1: Calculate the standardized test statistic \( t \)

The formula for the \( t \)-test statistic is \( t=\frac{\bar{x}-\mu}{s/\sqrt{n}} \).
Here, \( \bar{x} = 15.6\), \( \mu = 14.8\), \( s = 2.12\), and \( n = 21\).

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Step2: Determine the \( P \)-value

Using a \( t \)-distribution table or technology (such as a TI - 84 Plus: tcdf(lower, upper, df) where \( df=n - 1=21-1 = 20\), \( lower = 1.73\), \( upper=\infty\)), the \( P \)-value is found.
For \( t = 1.73\) and \( df=20\), the \( P \)-value \( P\approx0.049\) (using more accurate technology - based calculation).

Answer:

The standardized test statistic \( t\approx1.73\) and the \( P \)-value \( P\approx0.049\)