If you use a 0.05 level of significance in a two-tail hypothesis test, what decision will you make if ZSTAT=−1.78?Determine the decision rule. Select the correct choice below and fill in the answer box(es) within your choice.(Round to two decimal places as needed.) A. Reject H0 if ZSTAT>___. B. Reject H0 if ZSTAT<−__ or ZSTAT>+ __. C. Reject H0 ___ <ZSTAT<___. D. Reject H0 if ZSTAT<−___. The image shows a Z-table used for statistical calculations. This table provides the cumulative probability that a standard normal variable (Z) is less than or equal to a given value. It's structured in a grid format with Z-scores listed vertically on the leftmost column and the second decimal place listed horizontally across the top row. The intersection of each row and column gives the cumulative probability for that specific Z-score.**Explanation of Use:**- **Columns and Rows:** - The first column lists the Z-scores up to the first decimal (e.g., 0.0, 0.1, 0.2, etc.). - The top row represents the second decimal place of the Z-score (e.g., .00, .01, .02, etc.).- **Data Cells:** - Each cell in the table shows the cumulative probability, depicting the area under the curve to the left of the corresponding Z-score in a standard normal distribution.**Example:**To find the cumulative probability for a Z-score of 1.23:1. Find the row for Z = 1.2.2. Move across to the column for the second decimal place .03.3. The cell at this intersection shows the cumulative probability.Z-tables are essential tools in statistics, especially useful for hypothesis testing and confidence interval calculations. ### Standard Normal Distribution TableThe table shown is a standard normal distribution (Z) table which displays cumulative probabilities for a standard normal distribution. This is often used in statistics to find the probability that a statistic is observed below, above, or between values on the standard normal distribution.#### Structure of the Table:- **Rows & Columns:** - The first column on the left shows the Z-scores up to one decimal place (e.g., 0.0, 0.1, 0.2, etc.). - The top row shows the second decimal place of the Z-score (e.g., 0.01, 0.02, ... 0.09).- **Cumulative Probabilities:** - Each cell within the table represents the probability that a standard normal random variable is less than or equal to a particular Z-score. - For example, if you want to find the cumulative probability for a Z-score of 0.53, you locate the row for 0.5 and the column for 0.03, which gives the cumulative probability as 0.7019.#### How to Use the Table:1. **Identify the Z-Score:** Determine the Z-score for which you need the cumulative probability.2. **Find the Row:** Look at the first decimal place of the Z-score to find the appropriate row.3. **Find the Column:** Use the second decimal place to find the appropriate column under that row.4. **Locate the Probability:** The cell where the row and column intersect gives the cumulative probability.This table is essential for statistical analysis, particularly in hypothesis testing and confidence interval estimation, where understanding the distribution of data in relation to the mean becomes critical.

Given- α=0.05ZSTAT=-1.78 Decision Rule: If P(Z<ZSTAT)<α2, we reject the null hypothesis. (We multiply by 2 in the case of a two-tailed test) If P(Z<ZSTAT)>α2, we do not reject the null hypothesis. Here, P(Z<-1.78)=1-P(Z<1.78)=1-0.9625=0.0375 The probability of obtaining a more extreme value than the one obtained is 0.0375×2=0.075 which is greater than 0.05. So we do not reject the null hypothesis. Option A is incorrect. We reject H0 if ZSTAT> critical value in case of a right-tailed test. But here we have a two-tailed test. So the statement is invalid. Option B is correct. When carrying out a two-tailed test with α level of significance, if the ZSTAT lies in the range (-1.96,1.96), i.e, the upper and lower 2.5% points of the N(0,1) distribution, we accept the null hypothesis. If ZSTAT lies outside this range, we reject the null hypothesis. Here -1.96<1.78<1.96 So we accept H0. We would reject H0 if ZSTAT<-1.96 and ZSTAT>1.96 Option C is incorrect. If -1.96< ZSTAT<1.96, we accept H0. Option D is incorrect. We reject H0 if ZSTAT< -critical value in case of a left-tailed test, but here we have a two-tailed test. So the statement is invalid.