 Layla Velazquez

2022-07-01

How will you formulate the appropriate null and alternativehypotheses on a population mean. lodosr

Expert

Null Hypothesis - It states that there no relationship/difference between sample means or proportions. It is represented by ${H}_{0}$. It takes "=", "$\le$" or "$\ge$" operators depending on the wording of the hypotheses test.
Alternative Hypothesis is a claim about the population that is contradictory to ${H}_{0}$. It is represented by ${H}_{1}$. It takes "$\ne$", "<" or ">" operators depending on the wording of the hypotheses test.

Here, we test whether the mean of a population is statistically different from a known or hypothesized value (40).
This is a two tailed test, since the alternative hypothesis contains "$\ne$" symbol.
A right tailed test contains a greater than (>) symbol in the alternative hypothesis.
If we are asked to test if the population mean is greater than 40, we use a right tailed test.
Then, the null hypothesis states that the mean is less than or equal to 40. The alternative hypothesis would be that the mean is greater than 40.
A left tailed test contains a less than (<) symbol in the alternative hypothesis.
If we are asked to test if the population mean is less than 40, we use a left tailed test.
Then, the null hypothesis states that the mean is greater than or equal to 40. The alternative hypothesis would be that the mean is less than 40.

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