Listed below are the lead concentrations in muμ​g/g measured in different traditional medicines. Use a 0.010.01 significance level to test the claim that the mean lead concentration for all such medicines is less than 1717 muμ​g/g. Assume that the lead concentrations in traditional medicines are normally distributed.   1010      13.513.5      16.516.5      19.519.5      2121      13.513.5      3.53.5      22.522.5      1313      3.53.5    What are the null and alternative​ hypotheses?     A. Upper H 0H0​: muμequals=1717 muμ​g/g Upper H 1H1​: muμless than<1717 muμ​g/g   B. Upper H 0H0​: muμequals=1717 muμ​g/g Upper H 1H1​: muμgreater than>1717 muμ​g/g   C. Upper H 0H0​: muμequals=1717 muμ​g/g Upper H 1H1​: muμnot equals≠1717 muμ​g/g   D. Upper H 0H0​: muμgreater than>1717 muμ​g/g Upper H 1H1​: muμless than<1717 muμ​g/g Determine the test statistic.     ​(Round to two decimal places as​ needed.) Determine the​ P-value.     ​(Round to three decimal places as​ needed.) State the final conclusion that addresses the original claim.       Upper H 0H0. There is     evidence to conclude that the mean lead concentration for all such medicines is     1717 muμ​g/g

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.