data sample x contains 40 sample and the proposed hypothesis h commite 12 error find the value for a sample error and the true error given that zn for 40 sample is 95 percentage and the value is 1.96
Answers
Answer:
Explanation:
Upper-tailed, Lower-tailed, Two-tailed Tests
The research or alternative hypothesis can take one of three forms. An investigator might believe that the parameter has increased, decreased or changed. For example, an investigator might hypothesize:
H1: μ > μ 0 , where μ0 is the comparator or null value (e.g., μ0 =191 in our example about weight in men in 2006) and an increase is hypothesized - this type of test is called an upper-tailed test;
H1: μ < μ0 , where a decrease is hypothesized and this is called a lower-tailed test; or
H1: μ ≠ μ 0, where a difference is hypothesized and this is called a two-tailed test.
The exact form of the research hypothesis depends on the investigator's belief about the parameter of interest and whether it has possibly increased, decreased or is different from the null value. The research hypothesis is set up by the investigator before any data are collected.
Step 2. Select the appropriate test statistic.
The test statistic is a single number that summarizes the sample information. An example of a test statistic is the Z statistic computed as follows:
equation image indicator
When the sample size is small, we will use t statistics (just as we did when constructing confidence intervals for small samples). As we present each scenario, alternative test statistics are provided along with conditions for their appropriate use.
Step 3. Set up decision rule.
The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic (e.g., reject H0 if Z > 1.645). The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below.
The decision rule depends on whether an upper-tailed, lower-tailed, or two-tailed test is proposed. In an upper-tailed test the decision rule has investigators reject H0 if the test statistic is larger than the critical value. In a lower-tailed test the decision rule has investigators reject H0 if the test statistic is smaller than the critical value. In a two-tailed test the decision rule has investigators reject H0 if the test statistic is extreme, either larger than an upper critical value or smaller than a lower critical value.
The exact form of the test statistic is also important in determining the decision rule. If the test statistic follows the standard normal distribution (Z), then the decision rule will be based on the standard normal distribution. If the test statistic follows the t distribution, then the decision rule will be based on the t distribution. The appropriate critical value will be selected from the t distribution again depending on the specific alternative hypothesis and the level of significance.
The third factor is the level of significance. The level of significance which is selected in Step 1 (e.g., α =0.05) dictates the critical value. For example, in an upper tailed Z test, if α =0.05 then the critical value is Z=1.645.