Question

1a) Explain why we reject the null hypothesis when the p-value is less than the level of significance?

b) Explain to someone unfamiliar with statistics how to tell whether a statistical test is left, right, or two tailed. Explain what to look for in the wording of a hypothesis test and with the alternate hypothesis.

c) Why can we never truly accept the null hypothesis?

Answer 1

a) We reject the null hypothesis when the p-value is less than the level of significance because given the null hypothesis is true, a p-value is a probability of getting a result as or more extreme than the sample result by random chance alone. If a p-value is lower than our significance level, we reject the null hypothesis.

b) One-tailed hypothesis tests are also known as directional and one-sided tests because you can test for effects in only one direction.

A right-tailed test is where your hypothesis statement contains a greater than (>) symbol. In other words, the inequality points to the right. For example, you might be comparing the life of batteries before and after a manufacturing change. If you want to know if the battery life is greater than the original.

Similarly for left tailed test s where your hypothesis statement contains a lesser than (<) symbol. In other words, the inequality points to the left. For example, you might be comparing the life of batteries before and after a manufacturing change. If you want to know if the battery life is lesser than the original.

Two-tailed hypothesis tests are also known as nondirectional and two-sided tests because you can test for effects in both directions. We use a two-tailed test because we care whether the mean is greater than or less than ( i.e if it is equal or not ) to the target value.

c) accepting the null hypothesis means we are sure that the null hypothesis is true. but we cannot be sure. we are deciding only on the basis of the sample data. So we always say that we fail to reject the null hypothesis based on the sample evidence

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