49. A university has six colleges and takes a poll to gauge student support for a tuition increase. The university wants to ensure each college is represented fairly. The below table shows the observed number of students that participate in the poll from each college and the actual proportion of students in each college. College Observed Proportion 457 0.20 206 0.08 3 301 0.13 4 792 0.29 336 0.15 373 0.15 Using the critical value approach, the decision and conclusion are A. reject the null hypothesis; at least one of the proportions is different from its hypothesized value B. reject the null hypothesis; all of the proportions are not the same C. do not reject the null hypothesis; all proportions are equal to 0.20 D. do not reject the null hypothesis; we cannot conclude not all of the proportions are the same 50. In the following table, individuals are cross-classified by their age group and income level. Income Medium High Age 21-35 Low 120 100 75 36-50 51-65 150 160 100 160 180 160 Using the p-value approach and a = 0.05, the decision and conclusion are A. do not reject the null hypothesis; age and income are dependent B. do not reject the null hypothesis; age and income are independent C. reject the null hypothesis; age and income are dependent D. reject the null hypothesis; age and income are independent

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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.