cistG

2021-09-18

The Level of Significance of a Statistical Test The

a) Is there substantial evidence

b) What is the level of significance (p -value) of your test results?

c) What is the probability of a Type II error if the stain with the additive in fact has a mean absorption rate of 30?

d) Estimate the mean absorption using a 99% confidence interval. Is the confidence interval consistent with your conclusions from the test of hypotheses?

Bentley Leach

Skilled2021-09-19Added 109 answers

Step 1

a) As we are testing here whether the mean has decreased from the mean level of 35, therefore the null and the alternative hypothesis here are given as:

The test statistic here is computed as:

For

As the p-value here is high, we cannot reject the null hypothesis here and therefore we conclude here that the mean is not less than 35 units here.

b) The p-value above obtained is 0.1436.

c) For 49 degrees of freedom, we have from t distribution tables:

Therefore the critical mean value here is computed as:

The probability of type II error for a true mean of 30 is computed here as:

Converting it into a t distribution variable, we have here:

Getting it from the t distribution tables, we have here:

Therefore 0.0781 is the required probability here.

d) for the critical value obtained in previous part, the 99% confidence interval here is obtained as:

As the confidence interval here contains 35, therefore the test is not significant here and we cannot conclude here that the mean is less than 35.

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