Suppose $$H_0=$$ Null Hypothesis, $$H_a=$$ Alternate Hypothesis, $$\mu$$ = population mean, $$\mu H_0$$= hypothesized mean. A researcher sets up $$H_0:\mu=$$​  $$\mu_{H_0}$$ and $$H_a:\mu<\mu_{H_0}.$$ In this situation, the researchers would apply.

Correct option is B

In hypothesis testing:
· The null hypothesis (H₀) assumes that the population mean is equal to the hypothesized mean (H₀: μ = H₀).
· The alternate hypothesis (Hₐ) indicates a specific direction of deviation. Here, it states that the population mean is less than the hypothesized mean (Hₐ: μ < H₀).
A left-tailed test is used when the alternate hypothesis specifies that the population parameter is less than the hypothesized value. The rejection region for this test lies in the left tail of the distribution. The researcher assesses whether the test statistic falls in this region to decide whether to reject H₀.
Information Booster:
1. Hypothesis Tests:
· Left-tailed test: Hₐ: μ < H₀. Tests for values significantly less than the hypothesized mean.
· Right-tailed test: Hₐ: μ > H₀. Tests for values significantly greater than the hypothesized mean.
· Two-tailed test: Hₐ: μ ≠ H₀. Tests for any significant deviation (both higher or lower) from the hypothesized mean.
2. Critical Region: In a left-tailed test, the critical region is on the left side of the sampling distribution, determined by the significance level (e.g., α = 0.05).
3. Common Scenarios: Left-tailed tests are often used in situations like testing if a production process yields results below a minimum acceptable standard.