When the null hypothesis is accept and symbolically we can express as

Correct option is A

The null hypothesis ( H0H_0H0​) typically states that there is no difference or no relationship between certain parameters being tested.
1. When the null hypothesis is accepted, it indicates that the sample mean (μ\muμ) is statistically equal to the hypothesized population mean (μH0\mu_{H_0}μH0​​).
Symbolic Representation: · μ=μH0\mu = \mu_{H_0}μ=μH0​​ This implies that the observed data supports the null hypothesis.
Explanation of Other Options: · (b) μ≠μH0\mu \neq \mu_{H_0}μ=μH0​​:
· Represents the alternative hypothesis (HaH_aHa​), which states that the sample mean is not equal to the population mean.
· (c) μ>μH0\mu > \mu_{H_0}μ>μH0​​:
· Indicates a one-tailed test where the alternative hypothesis suggests the sample mean is greater than the hypothesized mean.
· (d) μ<μH0\mu < \mu_{H_0}μ<μH0​​:
· Indicates a one-tailed test where the alternative hypothesis suggests the sample mean is less than the hypothesized mean.
Correct Answer: (a) μ=μH0\mu = \mu_{H_0}μ=μH0​​ Information Booster 1. Null Hypothesis ( H0H_0H0​):
· Serves as the default or baseline assumption in hypothesis testing.
· Accepted when there is insufficient evidence to support the alternative hypothesis (HaH_aHa​).
2. Key Points in Hypothesis Testing:
· Two-tailed test: Tests whether μ≠μH0\mu \neq \mu_{H_0}μ=μH0​​.
· One-tailed test: Tests whether μ>μH0\mu > \mu_{H_0}μ>μH0​​ or μ<μH0\mu < \mu_{H_0}μ<μH0​​.
3. Applications:
· Used in research to evaluate statistical significance in experiments and surveys.