Question

b. the science department believes that the average time a lab computer takes to boot up is 45 seconds. students believe the computers have gotten slower and the real mean is greater than 45. $h_0: \mu = 45$; $h_a: \mu > 45$. evidence: a random sample of 25 computers. sample mean: $\bar{x}=48.1$ seconds. sample standard deviation: $s = 8$ seconds. $\hat{\mu} = \square$; unusualness: t.k. = $\square$ (three decimal places); chances: p - value = $\square$ (three decimal places).

Explanation:

Step1: Identify t-test formula

The t-statistic for one sample is $t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$

Step2: Plug in values

$\bar{x}=49.1$, $\mu_0=45$, $s=8$, $n=25$.
$t = \frac{49.1 - 45}{8/\sqrt{25}} = \frac{4.1}{8/5} = \frac{4.1}{1.6} = 2.5625$

Step3: Calculate degrees of freedom

$df = n - 1 = 25 - 1 = 24$

Step4: Find P-value (one-tailed)

Using t-distribution table or calculator for $t=2.5625$, $df=24$ (one-tailed), P-value ≈ 0.008

Answer:

t = 2.5625
Degrees of freedom = 24
P-value = 0.008