Question #4 ### Standard Normal Distribution and Chi-Square Distribution Tables#### Image OverviewThis image contains four distinct statistical tables, including tables of standard normal distribution and chi-square distribution. Each table is accompanied by a graph illustrating the distribution curve.#### Standard Normal Distribution (Top Tables)**Graphs:**- Both tables at the top are accompanied by bell-shaped graphs representing the standard normal distribution. The shaded area in the left tail of the curve is marked as "Area."**Table Description:**- The tables list the cumulative probabilities associated with z-scores from a standard normal distribution.- The columns represent different decimal increments of the z-score.- The first column on the left shows the integer and first decimal place of the z-score, while the subsequent columns display further decimal increments (e.g., 0.00, 0.01, 0.02, etc.). #### t-Distribution (Bottom Left Table)**Graph:**- The graph shows a similar bell-shaped curve labeled with "Area in Tail," indicating the portion of the distribution being tabulated.**Table Description:**- This table represents the t-distribution with varying degrees of freedom.- The first column lists the degrees of freedom (df).- The columns provide the t-values for different alpha levels (e.g., 0.25, 0.10, 0.05, etc.) for both one-tailed and two-tailed tests.#### Chi-Square Distribution (Bottom Right Table)**Graphs:**- Three different graphs are shown: - The first illustrates the chi-square distribution with a shaded right tail. - Annotations like "Right Tail" and specific alpha values depict the critical region. - The graphs emphasize the area under the curve to the right of the chi-square statistic.**Table Description:**- This table presents critical values of the chi-square distribution for various alpha levels.- The first column lists degrees of freedom.- Additional columns exhibit critical chi-square values corresponding to tail probabilities like 0.995, 0.99, 0.975, up to 0.005.- Each cell indicates the chi-square statistic threshold for rejecting the null hypothesis at the tailored significance level for a given degree of freedom.These tables are essential tools in hypothesis testing and statistical analysis, providing critical values to determine statistical significance in research. In a survey of 1012 adults, a polling agency asked, "When you retire, do you think you will have enough money to live comfortably or not. Of the 1012 surveyed, 529 stated that they were worried about having enough money to live comfortably in retirement. Construct a 95% confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement.- Click here to view the standard normal distribution table (page 1).- Click here to view the standard normal distribution table (page 2).- Click here to view the table of critical t-values.- Click here to view the table of critical values of the chi-square distribution.---Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to three decimal places as needed.)A. 95% of the population lies in the interval between ⬜ and ⬜.B. There is a 95% probability that the true proportion of worried adults is between ⬜ and ⬜.C. There is 95% confidence that the true proportion of worried adults is between ⬜ and ⬜.

Answered: Image /qna-images/answer/ce68d005-1f46-4a44-a1e6-0ed78609d295.jpgAssume that p is the true population proportion of adults who said that they are worried about having enough money to live comfortable in retirement and the point estimate of p is p̂ = x/n, such that, x is the number of favorable cases and n is the sample size. According to given question, in a sample of 1012 adults 529 said that they are worried about having enough money to live comfortable in retirement. That is, n = 1012, x = 529 and, p̂ = 529/1012 ≈ 0.522727. The confidence level is 95%. If 95% of the observations must lie within an interval, the remaining 5% must lie outside the interval. Further, due to symmetry, 2.5% will lie above the upper limit and the remaining 2.5% will lie below the lower limit of the interval. Thus, the upper limit of the interval is such that, 97.5% lie below it. As a result, from the standard normal table corresponding to row of 1.9 and column of .06, it is obtained that, zα/2 = z0.025 ≈ 1.96 [Using Excel formula: =NORM.S.INV(0.975)]. The confidence interval is, Thus, the 95% confidence interval estimate is 0.492 < p < 0.554. There is 95% confidence that the true proportion of worried adults is between 0.492 and 0.554. Correct option is C.

Math

Statistics

In a survey of 1012 adults, a polling agency asked, "When you retire, do you think you will have enough money to live comfortably or not. Of the 1012 surveyed, 529 stated that they were worried about having enough money to live comfortably in retirement. Construct a 95% confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). Click here to view the table of critical t-values. Click here to view the table of critical values of the chi-square distribution, Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to three decimal places as needed.) O A. 95% of the population lies in the interval between and. O B. There is a 95% probability that the true proportion of worried adults between and O C. There is 95% confidence that the true proportion of worried adults is between and