For the School Subject, what on earth is Res? I thought it asked for a resumé and that's the only reason I opened it! If you correctly label the School Subject, you will get the correct teacher faster.
Sra
A two-tailed hypothesis test at the 5 percent level of significance (£\ = .05) is exactly equivalent to asking whether the 95 percent confidence interval for the mean includes the hypothesized mean. If the confidence interval includes the hypothesized mean
H0: £g = 216, then we cannot reject the null hypothesis. Also, £m = .023
In this case the 95 percent confidence interval would be
¡x ¡Ó z£m¡Ôn = 216.007 ¡Ó 1.96 (.023)¡Ô50 = 216.001 < £g < 216.013
Since this confidence interval does not include 216, we reject the null hypothesis H0: £g = 216.
However, the decision is rather a close one as it was with the two-tailed hypothesis test, since the lower limit of the confidence interval almost includes 216.
Interpretation: Although the sample mean 216.007 might seem very close to 216, it is
more than two standard deviations from the desired mean. This example shows that even a small difference can be significant. It all depends on £m and n, that is, on the standard error of the mean in the denominator of the test statistic. In this case, there is a high degree of precision in the manufacturing process (£m = .023 is very small) so the standard error (and hence the allowable variation) is extremely small. Such a tiny difference in means would not be noticeable to consumers, but stringent quality control standards are applied to ensure that no shipment goes out with any noticeable non-conformance.
Please provide responses to the following:
(a) Give a brief example of a two-tailed hypothesis.
(b) Small differences can be statistical significant e.g. a high degree of precision in a manufacturing process. Give another example of where we can have such statistical significance with small differences.
(c) List the steps in the formal hypothesis testing process. Which step do you feel will be the most challenging for you? What does this challenging step involve?
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