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- A total of 205 people were asked to pick their favorite product from a list of three options. Consumers chose product A 83 times, B 75 times, and C 47 times. Is there enough evidence to say that the three products have different chances of being chosen? ? = 0.10A dairy farmer thinks that the average weight gain of his cows depends on two factors: the type of grain that they are fed and the type of grass that they are fed. The dairy farmer has four different types of grain from which to choose and three different types of grass from which to choose. He would like to determine if there is a particular combination of grain and grass that would lead to the greatest weight gain on average for his cows. He randomly selects three one-year-old cows and assigns them to each of the possible combinations of grain and grass. After one year he records the weight gain for each cow (in pounds) with the following results. Is there sufficient evidence to conclude that there is a significant difference in the average weight gains among the cows for the different types of grain? Cow Weight Gain (Pounds) Grass A Grass B Grass B Grain A 163163 287287 305305 267267 304304 325325 198198 348348 172172 Grain B 338338 291291 223223 286286 168168…In a certain class of 25 students, 12% received A’s, 30% received B’s, 42% received C’s, and 12% received D’s. How many students failed the class?
- Helen wants to compare two machines in her factory to see if the wrapping was satisfactory. She wants to know if there is a difference between the two machines. She randomly chooses 56 packs that were wrapped with machine A and finds among them 47 that were satisfactory. She also randomly chooses 25 packs that were wrapped by machine B and notices that 14 of them were satisfactory. Use this information for both parts.It has been discovered that a sub-species of animal, the Spotted Manumar, has 4 different blood types: M, N, P and MN. Type MN is uncommon: Only 10% of them have this type. The remaining 90% of the animals are equally split among the 3 other types. On another continent, there is another sub-species of the Manumar. The Furry Manumar also has the same 4 blood types and the researchers wonder if the proportions of bloodtypes matches that of the Spotted ones. If we hypothesized that the Furry ones did match the Spotted ones, and 200 Furry Manumars were to be collected at random, you'd expect the number that have bloodtype MN to be 1 and the number to have bloodtype M to beA theater has 12 seats in the first row. Each row, moving back, increases by two seats. How many seats are in row #22? Submit work for this problem!
- Sarah believes that completely cutting caffeine out of a person's diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah's claim at the 0.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. Numbers of Nights of Restful Sleep in a Four-Week Period With Caffeine 24 22 24 20…Q6 How many different ways are there to select a group of 4 out of 6 people for a cyber-sport team with 4 distinct roles?A dairy farmer thinks that the average weight gain of his cows depends on two factors: the type of grain that they are fed and the type of grass that they are fed. The dairy farmer has four different types of grain from which to choose and three different types of grass from which to choose. He would like to determine if there is a particular combination of grain and grass that would lead to the greatest weight gain on average for his cows. He randomly selects three one-year-old cows and assigns them to each of the possible combinations of grain and grass. After one year he records the weight gain for each cow (in pounds) with the following results. Is there sufficient evidence to conclude that there is a significant difference in the average weight gains among the cows for the different types of grain? Cow Weight Gain (Pounds) Grass A Grass B Grass B Grain A 359359 327327 232232 277277 250250 163163 191191 304304 216216 Grain B 331331 348348 176176 318318 205205…
- a strap is made up of 20 beads (4 yellow, 6 blue, 3red and 7 green. Calculate for the all possible arrangements of the beads.In an experiment, there are 5 possible conditions, and you would like each participant to receive 3 out of the 5. However, you are concerned about the possible effects of the order in which the conditions are experienced, so you want to use all possible permutations of the 3 conditions tested. Calculate the number of permutations.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 =…
