Question

A null and alternative hypothesis are given. Determine whether the hypothesis test is​ left-tailed, right-tailed, or​ two-tailed.

H0​:σ ≥ 66
Ha​: σ < 6

Answer 1

For the hypotheses given, assuming a typo correction to Ha: σ < 66, the hypothesis test would be left-tailed because the alternative hypothesis suggests the population standard deviation is less than 66.

Step-by-step explanation:

The null and alternative hypotheses are given as H0: σ ≥ 66 and Ha: σ < 6, with σ representing the population standard deviation. However, there seems to be a typo in the alternative hypothesis. Assuming we correct it to Ha: σ < 66, this configuration of hypotheses suggests that the hypothesis test is left-tailed. The alternative hypothesis (Ha) indicates the direction of the hypothesis test.

A left-tailed test is used when the alternative hypothesis contains a less-than symbol (<), suggesting that the test is looking for evidence that the population standard deviation is less than a certain value. In this case, we are testing whether the population standard deviation is less than 66. A right-tailed test would have an alternative hypothesis with a greater-than symbol (>), and a two-tailed test would have an alternative hypothesis with a not-equal-to symbol (≠).

Answer 2

The given hypothesis test with the null hypothesis stating that the standard deviation is greater than or equal to 66, and the alternative hypothesis indicating that the standard deviation is less than 66, is a left-tailed test.

Step-by-step explanation:

The null (H0) and alternative (Ha or H1) hypotheses are statements that are tested by statistical methods. In this case, the null hypothesis (H0) states that the standard deviation or variance (symbol σ) is greater than or equal to 66.

The alternative hypothesis (Ha) states that the standard deviation is less than 66. Since the alternative hypothesis specifically indicates a 'less than' condition, it tells us that the test is left-tailed.

This is because it is testing for the possibility of the parameter being lower than a certain value.