Of the 50 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
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- Researchers constructed two test sheets, each sheet including 20 photos of the faces of dog–owner pairs taken at a dog lovers' field festival. The 20 sets of dog–owner pairs on the two sheets were equivalent with respect to breed, diversity of appearance, and gender of owners. On the first sheet, the dogs were matched with their owners, while on the second sheet, the dogs and owners were deliberately mismatched. Three experiments were conducted, and in all experiments, subjects were asked to "choose the set of dog–owner pairs that resemble each other, Sheet 1 or Sheet 2," and were simply told the aim of the research was a "survey on dog–owner relationships." In the first experiment, the original sheets were shown to subjects; in the second experiment, just the "mouth region" of the owners was blacked out in all the pictures on both sheets; in the third experiment, just the "eye region" of the owners was blacked out. Subjects were assigned at random to the three experimental groups, and…Do people get stressed out when other people watch them work? To find out, Sean and Shelby recruited 30 volunteers to take part in an experiment. Fifteen of the subjects were randomly assigned to complete a word search puzzle while Sean and Shelby stood close by and visibly took notes. The remaining 15 were assigned to complete a word search puzzle while Sean and Shelby stood at a distance. After each subject completed the word search, they completed a second word search under the opposite treatment. The amount of time required to complete each puzzle was recorded for each subject. Explain why these are paired data. These are paired data because they result from Seanand Shelby recorded with Sean and Shelby standing close by and, during a separate time, while Sean and ShelbyA consumer agency wants to determine which of two laundry detergents, A or B, cleans clothes better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be 1.5. Assuming there is no difference in the two detergents, 200 simulated differences in sample mean ratings are displayed in the dotplot. Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other? Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that A is more effective…
- Hector is out on an archeological dig. He randomly selected 563 artifacts that he encountered at a particular site and found 271 were pottery shards. He knows that for the area that he is in the proportion of artifacts that are pottery shards is 0.45728242. What percent of artifacts, selected again 563 at a time from another site, would have a higher proportion of pottery shards than what Hector found? If Hector randomly moves to another site and agains randomly selected 563 artifacts, what is the probability that his new site will have less than a proportion of 0.41718112778927 pottery shards? Hector is looking for a site that is an ancient Greek battleground. He knows that in this area if he were to find a battle ground he would find somewhere between 257 and 314 pottery artifacts for every 563 randomly selected. What proportion of sites would be likely candidates for Greek battle sites?A researcher surveys 200 randomly selected college students to determine the number of education majors and mathematics majors. 16% of the students surveyed are education majors and 6% of the students surveyed are mathematics majors. 2% of the students are both education majors and mathematics majors. What percentage of the students surveyed are education majors or mathematics majors?In 1940, 2,000 women working in a factory were recruited into a study. Half of the women worked in manufacturing and half in administrative offices. The incidence of bone cancer through 1970 among the 1,000 women working in manufacturing was compared with that of 1,000 women working in administrative offices. Thirty of the women in manufacturing developed bone cancer as compared to 9 of the women in administrative offices. Identify what type of study this is.
- Let’s say a psychologist suspects that emotions affect people’s eating habits, but that the eating habits of anxious people are affected differently. Ten highly anxious subjects are randomly divided into two equal-sized groups, one of which views a horror movie while the other watches a comedy. Ten non-anxious control subjects are similarly divided. The number of ounces of popcorn eaten by each subject during the movie is recorded. How many independent variables are there in this design? Name each of the factors and levels (using appropriate descriptors from the paragraph): How many total conditions (groups) are there in this design? Name the dependent variable:A manufacturer of automobile shock absorbers was interested in comparing the durability of its shock absorbers with that of the shock absorbers produced by its biggest competitor. To make the comparison, one of the manufacturer's and one of the competitor's shock absorbers were randomly selected and installed on the rear wheels of each of six cars. After the cars had been driven 20,000 kilometres, the strength of each test shock absorbers was measured, coded and recorded. It is given that the population variances are equal for both groups. The results of the examination are shown in the Table below. Manufacturer's shock absorbers Car number 1 8.8 Competitor's shock absorbers 8.4 10.1 2 10.5 3 12.5 12.0 4 9.7 9.3 5 9.6 9.0 6 13.2 13.0 Determine whether there is sufficient evidence to conclude that there is a difference in the mean strength of the two types of shock absorbers after 20,000 kilometres of use by using a level of significance of 0.05.The manager of a theater that is open to residents of two towns, A and B, wants to know if the proportion of households from A that use the library is smaller than the proportion of households from B. In order to test this, the manager asks 45 households in A and 49 households in B whether anyone in their household had used the theater last summer. 23 of the households surveyed in A responded "yes", and 35 of the households in B responded "yes". Find the p-value that would be used to make a conclusion for this hypothesis test.
- A researcher working at Hershey's is interested in comparing two new chocolate bars: Chocolate Bar A versus Chocolate Bar B. The researcher expects the bars to be different in how much customers will eat per month. The researcher believes the more candy bars someone eats will indicate which one tastes the best. An experiment is designed to compare the two new bars. The number of candy bars eaten by one group of 8 people in a month is measured with Candy Bar A and then the number of candy bars eaten in the same month by another group of 8 participants is measured with Candy Bar B. Use the data below to determine if there is a difference in the consumption of the two candy bars. Candy Bar A Candy Bar B Number of Candy Bars eaten within a month 10, 30, 5, 35, 60, 3, 20, 30, 28, 27, 26, 27, 17, 25 12, 20 With a = .05, determine the critical value of t* that needs to be employed here. The value of the appropriate of t* is: 2.145 O 1.717 2.064 2.819 2.074 O The correct answer is not listed.For the purposes of a marketing research, a survey of 1000 women is conducted in a town. The results show that 52 % liked watching comedies, 45% liked watching fantasy movies and 60% liked watching romantic movies. In addition, 25% liked watching comedy and fantasy both, 28% liked watching romantic and fantasy both and 30% liked watching comedy and romantic movies both. 6% liked watching none of these movie genres. Find The number of women who like watching at least two of the given genresA national television channel posted the result of their web poll: 63 percent of Americans favor changing from gasoline to hydrogen fuel for cars". The survey question had been available for three days and 50000 viewers responded. Should we conclude that hydrogen-pwered cars are favored by a majority of Americans? Explain.