Loyalty cards ~ Records for the past several years show that 48% of customers at a local game shop use a customer loyalty card. Due to a recent promotion of the cards, the manager wants to know if the percentage has increased. The manager decides to take a simple random sample of 155 customers and finds that 91 of them used the customer loyalty card at their last transaction. Round all numeric results to 4 decimal places. 1. Write the hypotheses to test if the proportion of customers using the card has increased from 48%. H0: The proportion of customers using the card ? v increased. Ha: The proportion of customers using the card ? v increased. 2. Calculate the proportion of customers in the sample who used the loyalty card. I} = 3. Describe a setup for a simulation that would be appropriate in this situation and how the p-value can be calculated using the simulation results. To set up a simulation for this situation, we let each customer be represented with a card. We take 100 cards, black cards represent customers who use a loyalty card and and red cards represent customers who do not use the card. Shuffle the cards and draw with replacement cards representing the random sample of customers. Calculate the proportion of ? v cards in the sample and call itfysim. Repeat this process many, many times and plot the resulting sample proportions. The p-value will be the proportion of simulations where sh\" is ? v 4. Use the Bootstrap Test for a Single Proportion app to conduct the simulation. Draw at least 10000 samples, then report your p- value from the app. Use this external link to the Bootstrap Test for a Single Proportion if the app does not load properly on your computer. (Right click to open in a new tab or window.) Bootstrap Test for a Single Proportion Controls Instructions Graph Type Dotplot V Presets Custom V Null Parameter Value for Population Proportion 0.5 Sample Size 100 Number of Simulations 100 Construct the Null Distribution Reset C] Overlay Normal Curve C] Show Null Line C] Show Observed Line Samples Generated: 0 Count Proportions of Simulations further from null value than v Enter a Value C] Advanced Controls C] Show Theoretical Null Distribution Information p-value: 5. At the game shop in the neighboring town, the owners conduct a similar hypothesis test and calculate a p-value of 0.1622. How much evidence does this shop have that the null hypothesis model is not a good fit for their observed result? 0 A. Little 0 B. Some 0 C. Strong 0 D. Very Strong 0 E. Extremely Strong