ExtraCredit-05: Problem 2 Problem Value: 1 point(s). Problem Score: 0%. Attempts Remaining: Unlimited. (1 point) 401(k) ~ Suppose a recent random sample of employees nationwide that have a 401(k) retirement plan found that 22% of them had borrowed against it in the last year. A local company is interested in assessing whether this proportion adequately describes the borrowing behavior of their employees. They take a random sample of 110 employees and find that 20 had borrowed from their plan. Conduct a hypothesis test to investigate whether the borrowing rate at this company is different from the nationally reported figure of 22%. Round all numeric results to 4 decimal places. 1. Write the hypotheses to test if the proportion of employees borrowing from their plan is different from the percentage reported nationwide. Ho: The proportion of employees who have borrowed from their plan ? the 22% reported nationwide. The difference ? v due to chance. Ha: The proportion of employees who have borrowed from their plan ? the 22% reported nationwide. The difference ? due to chance . 2. Calculate the proportion of employees in the sample who borrowed from their retirement plan. P = 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 employee be represented with a card. We take 100 cards, green cards represent employees who have borrowed from their plan and white cards represent employees who have not. Shuffle the cards and draw with replacement cards representing the random sample of customers. Calculate the proportion of ? cards in the sample and call it P sim- Repeat this process many, many times and plot the resulting sample proportions. The p-value will be the proportion of simulations where P sim is ? 4. Use the One Proportion Resampling Test app to conduct the simulation. Draw at least 3000 samples, then report your p-value from the app. Use this external link to the One Proportion Resampling Test if the app does not load properly on your computer. (Right click to open in a new tab or window.)p-value: 5. Jackson is another small business owner. He uses the same hypotheses and data from his own company to conduct this test and calculates a p-value of 0.1008. How much evidence does Jackson have that the null hypothesis model is not a good fit for his observed result? OA. Little OB. Some O C. Strong OD. Very Strong O E. Extremely StrongExtraCredit-05: Problem 3 Problem Value: 1 point(s). Problem Score: 0%. Attempts Remaining: Unlimited. (1 point) An insurance company states that at least 88% of its claims are settled within 30 days. A consumer group selected a random sample of 68 of the company's claims to test this statement. They found that 55 of the claims were settled within 30 days. Does the consumer group have evidence to disbelieve the insurance company's claim? 1. Write the hypotheses to test if the rate of claims settled within 30 days is less than 88%. Ho: The proportion of claims settled within 30 days ? 88% HA: The proportion of claims settled within 30 days ? v 88% 2. To set up a simulation for this situation, we let each claim be represented with a card. We take 100 cards, green cards represent claims that are settled within 30 days and white cards represent claims that take longer than 30 days to settle. the cards and draw with replacement cards representing the random sample of claims. Calculate the proportion of ? cards in the sample and call it P sim- Repeat this process many, many times and plot the resulting sample proportions. The p-value will be the proportion of simulations where P sim is ? 3. Use the One Proportion Resampling Test app to conduct the simulation. Draw at least 3000 samples, then report your p-value from the app. Use this external link to the One Proportion Resampling Test if the app does not load properly on your computer. (Right click to open in a new tab or window.)p-value: 4. Charlene works for a non-profit organization that helps people navigate insurance claims. She conducts a similar hypothesis test using a different sample and calculates a p-value of 0.169. How much evidence does Charlene have against the null hypothesis? OA. Little OB. Some O C. Strong O D. Very Strong O E. Extremely StrongExtraCredit-05: Problem 5 Problem Value: 1 point(s). Problem Score: 0%. Attempts Remaining: Unlimited. (1 point) The Bald Eagle is the national symbol of the United States and is found all over North America. The wingspan of bald eagles can be modelled by a normal distribution with mean 2.05 meters and standard deviation 0.082 meters. The Southern Royal Albatross is a large seabird. They are one of the popular tourist attractions in the Otago Peninsula near Dunedin, NZ. The wingspan of southern royal albatrosses can be modelled by a normal distribution with mean 3.14 meters and standard deviation 0.052 meters. During their trip to the US, Charles, William and Harry spot a bald eagle called Baldy with a wingspan of 2.25 meters and during their NZ trip they spot a royal albatross called Alby with a wingspan of 3.3 meters. 1. Calculate the z-score for Baldy's wingspan. 2. Calculate the z-score for Alby's wingspan. 3. Based on the respective distributions, whose wingspan is larger? O A. Alby's O B. Baldy's O C. They are the same O D. Impossible to tell without more information. 4. What proportion of royal albatrosses have wingspan between 2.95 meters and 3.2 meters? 5. What percentage of bald eagles have wingspan more than 1.95 meters? % 6. What is the cutoff for the smallest 20% of royal albatrosses wingspans? 7. What is the wingspan for a royal albatross with a wingspan at the 60 percentile?ExtraCredit-05: Problem 6 Problem Value: 1 point(s). Problem Score: 0%. Attempts Remaining: Unlimited. (1 point) Triathlon times. In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Hermosa Beach Triathlon, where Leo competed in the Men, Ages 30 - 34 group while Mary competed in the Women, Ages 25 - 29 group. Leo completed the race in 4738 seconds, while Mary completed the race in 5739 seconds. Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them? Round all calculated answers to four decimal places Here is some information on the performance of their groups: The finishing times of the Men, Ages 30 - 34 group has a mean of 4328 seconds with a standard deviation of 593 seconds. The finishing times of the Women, Ages 25 - 29 group has a mean of 5257 seconds with a standard deviation of 838 seconds. The distributions of finishing times for both groups are approximately Normal. Remember: a better performance corresponds to a faster finish. 1. Write the short-hand for these two normal distributions. The Men, Ages 30 - 34 group has a distribution of N( The Women, Ages 25 - 29 group has a distribution of N( 2. What is the Z score for Leo's finishing time? z = 3. What is the Z score for Mary's finishing time? z = 4. Did Leo or Mary rank better in their respective groups? A. They ranked the same O B. Mary ranked better O C. Leo ranked better 5. What percent of the triathletes did Leo finish slower than in his group? %. 6. What percent of the triathletes did Mary finish faster than in her group? % 7. What is the cutoff time for the fastest 17% of athletes in the men's group, i.e. those who took the shortest 17% of time to finish? seconds 8. What is the cutoff time for the slowest 20% of athletes in the women's group? secondsExtraCredit-05: Problem 7 Problem Value: 1 point(s). Problem Score: 0%. Attempts Remaining: Unlimited. (1 point) Toyota Camry Prices ~ Historic data suggest that among US teens and young adults the demand for buying used Toyota Camry is high. Suppose that the price of a used Toyota Camry is normally distributed with an average price of $7302 and a standard deviation of $576. Enter all answers rounded to 4 decimal places. 1. What proportion of used Toyota Camrys cost between $7000 and $8400? 2. What proportion of used Toyota Camrys cost less than $7000? 3. Suppose you want to purchase a used Toyota Camry. What is the chance that a randomly selected used Toyota Camry would cost more than $8400? 4. What is the cutoff price of used Toyota Camry in the top 22% price range? 5. What is the price of used Toyota Camry at the 20th percentile