Discussions #11 Discussion Board Initial Post: Here are two scenarios that can be answered using an appropriate hypothesis test: One is a 1 sample t-test for a mean and the other is a 1 sample z-test for a proportion. 1. A company is criticized because only 13 of 43 people in management-level positions are women. The company explains that although this proportion is lower than it might wish, it's not surprising given that women make up only 40% of their industry. What do you think? 2. The run times for 20 participants at a local 5K race was x_=29.2 min with a standard deviation of s=5.67. ls there evidence that the true mean run time for all of the participants is below 30 minutes?A dotplot of the sample data appears to be symmetric with no outliers. Complete BOTH problems, ensuring to follow all 5-steps outlined in the readings. Pay special attention to explaining how you checked the conditions for the distribution that you name. Feel free to use StatCrunch to perform the calculations for you. The use of the formulas for this assignment is optional. You can choose to write your solution on paper and upload an image of your work, OR you may type out your solutions (but try to use the appropriate symbols in your response by using the \"insert math question" feature). Discussion #12 on P-Value Discussion on P-Value Let's play a game where I ip a coin. If the coin lands on Heads you win a $1, if it lands on Tails you lose a $1. I ip a coin 8 times and here is the results Tails Tails Tails Tails Tails Tails Tails Tails So you lost 8 times in a row and thus lose $8.00. Initial Post: Part1: Would you like to continue this game. Why or why not. Part 2: Calculate the P-value of getting 8 tails in a row assuming the coin is fair. Is it a big number or small? Part 3: Based on the P-Value you got above what would you conclude about your initial hypothesis that the coin is fair