Question

Determine the critical value or values for a one-mean z-test at the 6% significance level if the hypothesis test is left-tailed (Ha: μ < μ0). a) -1.645 b) 1.645 c) -2.054 d) 2.054

Answer 1

The correct critical value for a 6% significance level, left-tailed one-mean z-test is -1.645, as it places 6% in the left tail of the normal distribution.

Step-by-step explanation:

In a one-mean z-test, the critical value is determined by the significance level and the direction of the hypothesis test. At a 6% significance level for a left-tailed test (where the alternative hypothesis is ), we are interested in the z-value that puts 6% in the left tail of the normal distribution. According to standard z-tables, the critical z-value that corresponds to an area of 0.06 in the left tail is slightly more extreme than -1.645.

Therefore, the correct critical value for a 6% significance level, left-tailed test is -1.645. This is the value that has approximately 0.06 to its left and would be the cutoff for rejecting the null hypothesis. Rejecting the null hypothesis means that there is enough evidence to support the alternative hypothesis that the true mean is less than the hypothesized mean.

Answer 2

The critical value for a one-mean z-test at the 6% significance level for a left-tailed test is a) -1.645.

Step-by-step explanation:

The critical value for a left-tailed one-mean z-test at the 6% significance level is -1.645 (option a).

When conducting a hypothesis test with a left-tailed alternative hypothesis (Ha: μ < μ0), we compare the test statistic (z-value) to the critical value to make a decision.

If the test statistic is less than or equal to the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

Since the critical value for this test is -1.645, we reject the null hypothesis if the test statistic is less than -1.645.