AP Statistics
The sample size for question 3 part B (P1) was large enough for the simulation using the normal distribution in addition to the fact that the null hypothesis, which states that the data was normally-distributed, was true. More specifically, the values of Pm – Pc were 10,000, which was large enough to simulate using the standard distribution method. Furthermore, a histogram is an excellent method for summarizing a large quantity of data, especially when the value of data is greater than 10. The basis for using the normal distribution to solve question 3 part B (P1) is that the result of extensive data is always normally distributed.
Additionally, the accuracy of normal approximation results is always directly related to an increase in the sample size. Hence it was appropriate to use the method for computing the results for the question since the sample size was 10,000, and there were high chances that the results would have been accurate. The normal distribution also allows for ease of approximating probabilities with random values that are difficult to memorize or even challenging to calculate due to a broad range of possible answers. For instance, question 3, part B (1), had many potential solutions given that the range of the data was 10,000, thereby the use of normal distribution was valid for the exercise. Don't use plagiarised sources.Get your custom essay just from $11/page
On the other hand, question part C (P2) was related to the Chi – distribution since the degree of freedom for the chi-distribution was enormous, given the value of the data was 10, 000. Hence the chi-distribution curve resembled a standard distribution curve. Finally, the result for question part C (P2) will be impossible if there were no differences between the two categories of the retirement community. Similarly, it will be impossible to obtain results using Chi-distribution if the data have no difference.