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. (a) identify the claim and state $h_0$ and $h_a$. $h_0$: $\mu \leq 14.7$ $h_a$: $\mu > 14.7$ (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.

Step2: Identify the values

We are given that \(\bar{x} = 15.5\), \(\mu=14.7\), \(s = 2.11\), and \(n = 22\).

Step3: Substitute the values into the formula

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First, calculate \(\sqrt{22}\approx4.69\), then \(2.11/\sqrt{22}\approx2.11/4.69\approx0.45\)

$$ t=\frac{0.8}{0.45}\approx1.78 $$

Answer:

\(t = 1.78\)