Question

1. claim: the average number of jokes people tell at a party is more than 10. so your hypotheses are: \\( h_0: mu = 10 \\) \\( h_a: mu > 10 \\) you surveyed 25 people and found that the average number of jokes told at a party was 10.5 with a standard deviation of 3. fill in the following(round 2 decimal places): mean \\( \square \\) mu(\\( \mu \\)) \\( \square \\) sd \\( \square \\) 1.5 \\( \square \\) assuming the null is true, would this be weird? type yes or no \\( \square \\)

Explanation:

Step1: Identify μ, x̄, s, n

μ = 10 (hypothesized mean), x̄ = 10.5 (sample mean), s = 1 (sample standard deviation), n = 25 (sample size)

Step2: Calculate t-statistic

Formula: $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$
Substitute values: $t = \frac{10.5 - 10}{\frac{1}{\sqrt{25}}} = \frac{0.5}{0.2} = 2.50$

Step3: Determine df

df = n - 1 = 25 - 1 = 24

Step4: Find p-value (one-tailed)

For t=2.50, df=24, one-tailed p-value ≈ 0.0098 (from t-table or calculator)

Step5: Check if weird (p<0.05)

0.0098 < 0.05 → yes

Answer:

μ: 10
x̄: 10.5
s: 1
n: 25
t: 2.50
df: 24
p-value: 0.0098
Assuming null is true, weird? Yes