Question

a consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.7 seconds. a random sample of 22 sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.11 seconds. at \\( \alpha = 0.10 \\) is there enough evidence to support the consumer groups claim? complete parts (a) through (d) below. assume the population is normally distributed.
the claim is the alternative hypothesis.
(b) use technology to find the p - value. find the standardized test statistic, t.
\\( t = 1.78 \\)
(round to two decimal places as needed.)
obtain the p - value.
\\( p = 0.044 \\)
(round to three decimal places as needed.)
(c) decide whether to reject or fail to reject the null hypothesis.
reject \\( h _ { 0 } \\) because the p - value is not greater than \\( \alpha \\).
(d) interpret the decision in the context of the original claim.
there \\( \square \\) enough evidence at the \\( \square \\% \\) level of significance to \\( \square \\) the claim that the mean minimum time it takes for a sedan to travel a quarter mile is \\( \square \\) seconds.
(type integers or decimals. do not round.)

Explanation:

Step1: Analyze the decision rule

In hypothesis testing, if \(P - value\leq\alpha\), we reject the null hypothesis \(H_0\). Here, \(\alpha = 0.10\) and \(P=0.044\). Since \(0.044<0.10\), we reject \(H_0\).

Step2: Interpret the result in context

When we reject \(H_0\), it means there is sufficient evidence to support the alternative hypothesis. The alternative hypothesis is the consumer - group's claim.

Answer:

There is enough evidence at the \(10\%\) level of significance to support the claim that the mean minimum time it takes for a sedan to travel a quarter mile is greater than \(14.7\) seconds.