Question

1. teachers think that the average time students spend on homework each night is 8 hours per week. a student group believes this is not accurate - it could be higher or lower. \\( h_0: mu = 8 \\) \\( h_a: mu \

eq 8 \\) evidence: a random sample of 40 students is taken. their average homework time is 9.1 hours with a standard deviation of 3.6 hours. \\( \bar{x} = \square \\) unstandardized t, t = \square (three decimal places) one - tailed p - value = \square (three decimal places)

Explanation:

Step1: Identify test type and parameters

This is a one-sample t-test. Given: $\mu_0 = 8$, $\bar{x} = 9.1$, $s = 3.8$, $n = 40$.

Step2: Calculate t-statistic

Formula: $t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$
Compute: $s/\sqrt{n} = 3.8/\sqrt{40} \approx 3.8/6.3246 \approx 0.6008$
$t = (9.1 - 8)/0.6008 \approx 1.1/0.6008 \approx 1.831$

Step3: Find degrees of freedom

$df = n - 1 = 40 - 1 = 39$

Step4: Calculate two-tailed p-value

Using t-distribution with $t=1.831$ and $df=39$, the two-tailed p-value is approximately 0.074.

Answer:

t = 1.83
Unrounded t = 1.831
Corrected P-value = 0.074