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: mu = 14.5 )
( h_a: mu > 14.5 )
(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=square )
(round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for the t - statistic

The formula for the t - statistic in a one - sample t - test is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(\mu\) is the hypothesized population mean, \(s\) is the sample standard deviation, and \(n\) is the sample size.
Given \(\bar{x} = 15.4\), \(\mu=14.5\), \(s = 2.12\), and \(n = 22\).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

First, calculate \(\sqrt{22}\approx4.69\), then \(2.12/\sqrt{22}\approx2.12/4.69\approx0.452\)

$$ t=\frac{0.9}{0.452}\approx1.99 $$

Answer:

\(t\approx2.0\) (rounded to one decimal place)