Two construction contracts are to be randomly assigned to one or more of three firms: 1, II, and I11. Any firm may receive both contracts. If each contract will yield a profit of $102,000 for the firm, find the expected profit for firm 1. If firms I and II are actually owned by the same individual, what is the owner's expected total profit?
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- The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same 8 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. Day 1 2 3 4 5 6 7 8 Store 1 889 699 534 398 432 213 252 929 Store 2 479 525 252 364 160 32 234 632 Difference(Store 1 - Store 2) 410 174 282 34 272 181 18 297 Send data to calculator Based on these data, can the owner conclude, at the 0.10 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding μd (which is μ…The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same 12 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. 5 6 7 Day Store 1 Store 2 1 Difference (Store 1 - Store 2) Send data to calculator ✓ 2 3 786 878 827 645 708 500 699 140 Yes No 4 646 802 712 579 527 367 76 115 66 181 133 8 (a) State the null hypothesis H and the alternative hypothesis H₁. H:D H₁:0 (b) Determine the type of test statistic to use. Type of test statistic: (Choose one) ▼ 970 9 10 11 12 618 679 762 635 271 572 324 215 698 530 Based on these data, can the owner conclude, at the 0.05 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis…The values listed below are waiting times (in minutes) of customers at two different banks. At Bank A, customers enter a single waiting line that feeds three teller windows. At Bank B, customers may enter any one of three different lines that have formed at three teller windows. Answer the following questions. Bank A 6.3 6.6 6.7 6.8 7.1 7.3 7.5 7.8 7.8 7.8 Bank B 4.2 5.5 5.9 6.3 6.7 7.7 7.7 8.5 9.3 10.0 Click the icon to view the table of Chi-Square critical values. Construct a 90% confidence interval for the population standard deviation o at Bank A. 7:6
- Suppose the entire cola industry produces only two colas. Given that a person last purchased cola 1, there a 70% chance that her next purchase will be cola 1. Given that a person last purchased cola 2, there is an 75% chance that her next purchase will be cola 2. Suppose that each customer makes one purchase of cola during any week (52 weeks=1 year). Suppose there are 150 million customers. One selling unit of cola costs the company $0.5 to produce and is sold for $2. For $200 million per year, Britney Spears (by an advertising song) guarantees to decrease from 30% to 15% the fraction of cola 1 customers who switch to cola 2 after a purchase. Should the company that makes cola 1 hire Britney Spears?The Harriet Hotel in downtown Boston has 100 rooms that rent for $150 per night. It costs the hotel $30 per room in variable costs (cleaning, bathroom items, etc.) each night a room is occupied. For each reservation accepted, there is a 5% chance that the guest will not arrive. If the hotel overbooks, it costs $200 to compensate guests whose reservations cannot be honored. How many reservations should the hotel accept if it wants to maximize the average daily profit?A chef is trying out a new recipe he has been working on and wants to see if it will sell better than his old one. To find out, he performs an experiment where he randomly assigns 20 people to try his new recipe and 20 people to try his old one. He asks each group how much they would be willing to pay for their food, and he finds that the group with the old recipe would pay an average of $20.00 and the second would pay an average of $26.00. He then performs an independent samples t-test between these groups. a. Suppose the sample variance for the price of the chef’s old recipe is $2.00, and the sample variance for the new recipe is $3.00. Perform a one-tailed t-test at a significance level of α = 0.01 and explain what the result means (how does the new recipe compare to the old one?). b. To evaluate the magnitude of effect size, compute the estimated Cohen’s d. Briefly describe what it means, and comment on the strength of the effect: is it weak, moderate or strong?
- Suppose that a region has two hospitals. Hospital A has about 10 births per day, and hospital B has about 50 births per day. About 50% of all babies are boys, but the percentage who are boys varies at each hospital from day to day. Over the course of a year, which hospital will have more days on which 60% or more of the births are boys? The smaller Hospital A, the larger B, or will Hospital A and B have nearly the same number of days?A gambler can roll a fair die up to four times. Before each roll, he must decide whether to roll one more time orstop the game and collect: his payoff is a doubled amount of the last score (e.g., if the last score is 3, he can collect$6). Each roll costs $3. Find the optimal roll/stop strategy that maximizes his expected gain.Mateo believes that completely cutting caffeine out of a person's diet will allow them more restful sleep at night. He randomly selects 8 adults to help him test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days and then cut back to no caffeinated bevarages for an additional 28 days. During each period, the participants record the number of nights of restful sleep that they had. The following table gives the results of the study. Test Mateo's claim at the 0.05 level of significance. Give answers to 4 decimal places as needed. Number of Nights of Restful Sleep in a Four-Week Period 15 With Caffeine 21 20 22 24 18 21 24 20 26 26 22 21 23 27 23 Without Caffeine a) The normal probability plot showed the differences follow a normal distribution and the boxplot showed no outliers. b) Test the claim (1) Determine the null and alternative hypotheses. Enter correct symbol and values Ho: H₁: (2) Type of test: (3) a = (4) Test statistic (to) = p-value =…
- You randomly recruit 23 students and tell each of them to come to the lab in two different mornings: each morning they will be offered some breakfast and will take a test. Each student will receive the light breakfast one time and the nutritious breakfast the other time (some will receive the light breakfast first, the others will receive the nutritious breakfast first, and the second time they switch). The average difference in a student’s score after eating the nutritious breakfast and their score after eating a light breakfast is 4.5, and the standard deviation of this difference is 3.6. (a) Construct a 95% confidence interval for the difference in the average score of students after having a nutritious breakfast and the average score of students after having a light breakfast.On the Great Stark island, the likelihood of a residential fire is evenly distributed at 12 per month. Residents are evenly distributed along the 64-mile perimeter of the island. The government is providing fire protection, and a fire department's fixed cost is $60,000 per month. If the travel cost to fight a fire is $2,500 per mile, what is the optimal number of fire departments?
