Question

a consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.5 seconds. a random sample of 22 sedans has a mean minimum time to travel a quarter mile of 15.4 seconds and a standard deviation of 2.12 seconds. at α = 0.10 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 ):
( h_a ):
(type integers or decimals. do not round.)
the claim is the hypothesis

Explanation:

Step1: Identify the claim

The claim is that the mean minimum time it takes for a sedan to travel a quarter - mile is greater than 14.5 seconds.

Step2: Set up the null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. So, \(H_0:\mu\leq14.5\).
The alternative hypothesis \(H_a\) is the claim. So, \(H_a:\mu > 14.5\).

Step3: Determine which hypothesis is the claim

Since the claim is \(H_a:\mu > 14.5\), the claim is the alternative hypothesis.

Answer:

\(H_0:\mu\leq14.5\), \(H_a:\mu > 14.5\), and the claim is the alternative hypothesis.