State whether each standardized test statistic chi squared   allows you to reject the null hypothesis. Explain.                   025 chi squared chi Subscript 0 Superscript 2 Baseline equals 18.3070               A coordinate system has a horizontal axis labeled chi squared from 0 to 25 in increments of 5 and a vertical axis. A curve is over a horizontal axis. Vertical line segment extends from the horizontal axis to the curve at chi Subscript 0 Superscript 2=18.3070. The area under the curve to the right of chi Subscript 0 Superscript 2=18.3070 is shaded. ​(a) chi squared equals12.243 ​(b) chi squared equals 0   ​(c) chi squared equals1.922 ​(d) chi squared equals18.296   ​(a) Choose the correct answer below.     A. Do not reject the null hypothesis because the standardized test statistic is in the rejection region.   B. Reject the null hypothesis because the standardized test statistic is not in the rejection region.   C. Do not reject the null hypothesis because the standardized test statistic is not in the rejection region.   D. Reject the null hypothesis because the standardized test statistic is in the rejection region. ​(b) Choose the correct answer below.     A. Do not reject the null hypothesis because the standardized test statistic is in the rejection region.   B. Do not reject the null hypothesis because the standardized test statistic is not in the rejection region.   C. Reject the null hypothesis because the standardized test statistic is in the rejection region.   D. Reject the null hypothesis because the standardized test statistic is not in the rejection region. ​(c) Choose the correct answer below.     A. Do not reject the null hypothesis because the standardized test statistic is not in the rejection region.   B. Do not reject the null hypothesis because the standardized test statistic is in the rejection region.   C. Reject the null hypothesis because the standardized test statistic is in the rejection region.   D. Reject the null hypothesis because the standardized test statistic is not in the rejection region. ​(d) Choose the correct answer below.     A. Do not reject   the null hypothesis because the standardized test statistic is not   in the rejection region.   B. Reject   the null hypothesis because the standardized test statistic is   in the rejection region.   C. Reject   the null hypothesis because the standardized test statistic is not   in the rejection region.   D. Do not reject   the null hypothesis because the standardized test statistic is   in the rejection region.

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!