If $$ H_{0}: \mu \geq 20, H_{a}: \mu

Question

If $$ H_{0}: \mu \geq 20, H_{a}: \mu<20 $$ and $$ \alpha=0.05 $$ and p -value $$ =0.0002 $$ then we failed to reject Null hypotheses

UpStudy AI · Accepted Answer

**Step 1: State the hypotheses.**

The null hypothesis is 
$$
H_0: \mu \ge 20,
$$
and the alternative hypothesis is 
$$
H_a: \mu < 20.
$$

**Step 2: Identify the significance level.**

The significance level is 
$$
\alpha = 0.05.
$$

**Step 3: Compare the p-value with the significance level.**

Given the p-value is 
$$
0.0002,
$$
and since 
$$
0.0002 < 0.05,
$$
we have strong evidence against the null hypothesis.

**Step 4: State the decision rule.**

If the p-value is less than the significance level ($$p < \alpha$$), we reject the null hypothesis.

**Step 5: Make the decision.**

Since 
$$
0.0002 < 0.05,
$$
we **reject** the null hypothesis $$H_0$$.

**Conclusion:**

The statement "we failed to reject the null hypothesis" is incorrect. In this case, we reject the null hypothesis.
We reject the null hypothesis because the p-value (0.0002) is less than the significance level (0.05).

If and and p -value then we failed
to reject Null hypotheses

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