Question

Let μ be the true average nicotine content of a brand of cigarettes whose nicotine content may reasonably be assumed Normally distributed with σ = 0.2. Suppose the observed sample mean of the nicotine content from 32 randomly selected cigarettes: = 1.4. Find the p-value associated with the following hypothesis: Ho : μ = 1.5 vs. HA : μ 1.5 What do you conclude?

Answer 1

Given that, sample size ( n ) = 32

sample mean $(\bar x)$ = 1.4

population standard deviation $(\sigma)$ = 0.2

The null and the alternative hypotheses are,

$H_0:\mu =1.5 \text { vs. } H_A: \mu \neq 1.5$

Test statistic is,

$Z = \frac {\bar x -\mu}{\frac {\sigma}{\sqrt n}}= \frac { 1.4-1.5}{\frac { 0.2}{\sqrt {32}}}= -2.83$

p-value = 2 * P(Z < -2.83) = 2 * 0.0023 = 0.0046

p-value = 0.0046

Here, p-value = 0.0046 < significance level $(\alpha)$ = 0.05

So, we reject the null hypothesis ( H₀).