1) Consider a game where you role three fair dice and count the total. The dice are eight, ten and twelve sided respectively. (a) Write an R function that will compute one round of this game. Have it return the values of the three dice and their total. Store the dice roles by the number of sides of the dice (smallest to largest). (b) Using the code in (a) write a function that will simulate n rounds of the game. (c) Suppose you win another role if the total of the three dice roles is less than or equal to 14. Write an R function that will compute the proportion of roles that meet this criteria after n rounds.
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- A rodentologist investigating various aspects of the aging process wanted to see whether staying “lean and mean” that is, being under normal body weight would lengthen life span. She randomly assigned newborn rats from a highly inbred line to one of three diets: (1) unlimited access to food, (2) 90% of the amount of food that a rat of that size would normally eat, (3) 80% of the amount of food that a rat of that size would normally eat. She maintained the rats on the three diets throughout their lives and recorded their life spans (in years). Complete a Turkey's post HOC test to determine which one is significantly differentAn agricultural scientist tests six types of fertilizer, labeled A, B, C, D, E, and F, to determine whether any of them produces an increase in the yield of lima beans over that obtained with the current fertilizer. For fertilizer C, the increase in yield is statistically significant at the 0.05 level. For the other five, the increase is not statistically significant. The scientist concludes that the yield obtained with fertilizer C is greater than that of the current fertilizer. Explain why this conclusion is not justified.According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers, 6 comma 0006,000 roaches (the expected number in a roach-infested house) were released in the test kitchen. One week later, the kitchen was fumigated and 18 comma 10718,107 dead roaches were counted, a gain of 12 comma 10712,107 roaches for the 1-week period. Assume that none of the original roaches died during the 1-week period and that the standard deviation of x, the number of roaches produced per roach in a 1-week period, is 1.61.6. Use the number of roaches produced by the sample of 6 comma 0006,000 roaches to find a 9595% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house. Find a 95% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house.
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- If there is no seasonal effect on people getting sick, we would expect equal numbers of people getting sick in each season (winter, spring, summer and fall). A student takes a census of students who took Marketing Research in 2019 and finds that of the 280 students who took Marketing Research in 2019, 75 were sick in winter, 65 were sick in spring, 68 were sick in summer and 72 were sick in fall. She wonders if the excess in the winter is an indication that sickness rates are not uniform throughout the year. Perform the appropriate chi-square test and indicate the chi-square value below. (Report two decimals)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 10 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. 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 test regarding μd (which is μ with a letter "d" subscript), the population mean daily sales difference between the two stores. Assume that this population of differences (Store 1 minus Store 2) is normally distributed. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If…