The following data set is composed of incidence rates of Kaposi’s sarcoma in 20 different regions of Tanzania. Reported in cases/million/year. 6.1, 6.6, 6.4, 6.6, 6.6, 7.6, 8.4, 8.5, 6.2, 7.6, 8.0, 7.3, 8.4, 6.6, 5.2, 6.2, 6.5, 5.8, 6.0, 6.1 Let μ be the true incident rate of Kaposi’s sarcoma in Tanzania is cases/million/year. If the true incident rate of Kaposi’s sarcoma in the United States is 6 cases/million/year based on a nationwide surveillance in 2014. Test whether the rate of Kaposi’s sarcoma in Tanzania is different from the United States at the 0.05 significance level. Be sure to state the null and alternative hypothesis. Carry out the appropriate hypothesis test by hand (you can also use SAS) and report the test statistic and the p-value and your conclusion in the context of the problem. What assumptions do we need for the validity of this hypothesis test?
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.
- The following data set is composed of incidence rates of Kaposi’s sarcoma in 20 different regions of Tanzania. Reported in cases/million/year.
6.1, 6.6, 6.4, 6.6, 6.6, 7.6, 8.4, 8.5, 6.2, 7.6, 8.0, 7.3, 8.4, 6.6, 5.2, 6.2, 6.5, 5.8, 6.0, 6.1
Let μ be the true incident rate of Kaposi’s sarcoma in Tanzania is cases/million/year. If the true incident rate of Kaposi’s sarcoma in the United States is 6 cases/million/year based on a nationwide surveillance in 2014. Test whether the rate of Kaposi’s sarcoma in Tanzania is different from the United States at the 0.05 significance level.
- Be sure to state the null and alternative hypothesis.
- Carry out the appropriate hypothesis test by hand (you can also use SAS) and report the test statistic and the p-value and your conclusion in the context of the problem.
- What assumptions do we need for the validity of this hypothesis test?
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