Listed below are the numbers of years that archbishops and monarchs in a certain country lived after their election or coronation. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.10 significance level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation. All measurement years. E Click the icon to view the table of longevities of archbishops and monarchs. What are the null and alternative hypotheses? Assume that population 1 consists of the longevity of archbishops and population 2 consists of the longevity of monarchs. O A. Ho: H1 *P2 O B. Ho: H1 S2 H: H >H2 OC. Ho: H1 = P2 O D. Ho: H1 = H2 H: 4 P2 The test statistic is . (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. O A. Reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs. O B. Reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs. OC. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs. O D. Fail to reject the null hypothesis. There is not sufficient evidence support the claim that archbishops have lower mean longevity than monarchs.

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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.