An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Determine that the problem is a two-tailed test.
Find the upper-tail critical z-value for a significance level of 2.5%, which is 1.96.
Determine that the critical values are -1.96 and 1.96.
The critical values for z in this study are − 1.96 and 1.96 .
Explanation
Analyze the problem The problem asks for the critical values of z for a two-tailed test with a significance level of 5% . The table provides upper-tail critical z -values. Since it's a two-tailed test, we need to find the z -values that correspond to the upper and lower tails, each containing 2.5% of the distribution.
Find the upper-tail critical z-value From the table, the upper-tail critical z -value for a significance level of 2.5% is 1.96 .
Determine the critical values Since it's a two-tailed test, the critical values are − 1.96 and 1.96 .
Examples
In hypothesis testing, critical values help determine whether to reject the null hypothesis. For example, if we are testing whether there is a significant difference in the average test scores of two groups, we would compare our test statistic to the critical values. If the test statistic falls outside the range of the critical values, we would reject the null hypothesis and conclude that there is a significant difference between the groups. The critical values depend on the significance level and the type of test (one-tailed or two-tailed).
