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?
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:
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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78038 18022 84755 23146 12720 70910 49732 79606
Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?
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1) 9 Hours
2) 3.5 Hours
3) 6 Hours
4) 12.5 Hours
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