Discussion #10 Tests of Significance Applying Hypothesis Tests For this discussi
ID: 3067122 • Letter: D
Question
Discussion #10 Tests of Significance Applying Hypothesis Tests For this discussion, you will need to post your response, as well as comment on at least two other posts. 1. How would you explain to someone who doesn't understand statistics the difference between confidence intervals and hypothesis testing? 2. Find a research article that uses a hypothesis test. Give either the reference for it or the website address at which you found it. Discuss what the research was trying to show, as well as the results from the test. Note that others have not read your article so you'll need to give a little bit of background information.Explanation / Answer
Hypothesis testing :
Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to infer the result of a hypothesis performed on sample data from a larger population.
Confidence interval :
Statisticians use a confidence interval to express the degree of uncertainty associated with a sample statistic. A confidence interval is an interval estimate combined with a probability statement.
Difference :
Now we have to construct a hypothesis testing problem.
Ex. An engineer measured the Brinell hardness of 25 pieces of ductile iron that were subcritically annealed. The resulting data were:
The engineer hypothesized that the mean Brinell hardness of all such ductile iron pieces is greater than 170. Therefore, he was interested in testing the hypotheses:
H0 : ? = 170
HA : ? > 170
The engineer entered his data into Minitab and requested that the "one-sample t-test" be conducted for the above hypotheses. He obtained the following output:
The output tells us that the average Brinell hardness of the n = 25 pieces of ductile iron was 172.52 with a standard deviation of 10.31. (The standard error of the mean "SE Mean", calculated by dividing the standard deviation 10.31 by the square root of n = 25, is 2.06). The test statistic t* is 1.22, and the P-value is 0.117.
If the engineer set his significance level ? at 0.05 and used the critical value approach to conduct his hypothesis test, he would reject the null hypothesis if his test statistic t* were greater than 1.7109
Since the engineer's test statistic, t* = 1.22, is not greater than 1.7109, the engineer fails to reject the null hypothesis. That is, the test statistic does not fall in the "critical region." There is insufficient evidence, at the ? = 0.05 level, to conclude that the mean Brinell hardness of all such ductile iron pieces is greater than 170.
If the engineer used the P-value approach to conduct his hypothesis test, he would determine the area under a
tn - 1 = t24 curve and to the right of the test statistic t* = 1.22:
In the output above, Minitab reports that the P-value is 0.117. Since the P-value, 0.117, is greater than ? = 0.05, the engineer fails to reject the null hypothesis. There is insufficient evidence, at the ? = 0.05 level, to conclude that the mean Brinell hardness of all such ductile iron pieces is greater than 170.
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