Question

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NEED ANSWER ASAP

(Hypothesis testing)

What do we need to consider when we try to select a test?

Choose one of the tests; discuss your understandings of that test. Use some examples to demonstrate your understanding.

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Answer 1

ANSWER:

The first consideration is the suitability of the test for the data. It involves size of the sample, number of samples to be tested and the confidence interval. For example, if sample size is less than 30, then t test is applied. If sample size is 30 or bigger, then Z test is applied. For analysis of variance, ANOVA test is applied. Further, for two samples, two sample test is applied. Similarly, two way ANOVA or one way ANOVA test is used depending upon the data and its requirements. The second consideration is the direction of the data for testing. It is either greater or lesser than hypothesis or equal to or not equal to hypothesis. Accordingly, the test is chosen to test the significance.

For the discussion, Z test is chose to identify the difference is significant or non-significant. Here, the sample size is more than 30. The value of Z is calculated by the following formula:

Z = (X - µ)/SE

X = Observed mean

µ = standard mean

SD = standard deviation

SE = Standard Error = S.D./(sample size)^.5

Value of Z = calculated and the area covered is identified with normal distribution table. If the value of Z is greater than the significant level value (95% or 90% or any other value). Then Alternative hypothesis is accepted. Otherwise null hypothesis is accepted.

Consider the following example:

Same size of the bulb = 100

Mean life time = 1580 hours

SD = 90 hours

Observed life time = 1600 hours

Test the significance of the difference at 95% confidence interval.

Null hypothesis: there is no significant difference X = µ

Alternative hypothesis: there is a significant difference X ≠ µ

It is a two tailed test.

Z = (1600 – 1580)/(90/100^.5) = 2.22

Area covered under Z is .9868 or .4934 each side and it is greater than the .475 each side. So, alternative hypothesis is correct and there is significant difference.