A graduate student conducted an experiment in which 23 ten-month-old babies were asked to watch a climber character attempt to ascend a hill. On two​ occasions, the baby witnesses the character fail to make the climb. On the third​ attempt, the baby witnesses either a helper toy push the character up the hill or a hinderer toy prevent the character from making the ascent. The helper and hinderer toys were shown to each baby in a random fashion for a fixed amount of time. The baby was then placed in front of each toy and allowed to choose which toy he or she wished to play with. In 20 of the 23 cases, the baby chose the helper toy. Use the binomial probability formula to determine the​ P-value for this test.

Many animals, including humans, tend to avoid directeye contact and even patterns that look like eyes.Some insects, including moths, have evolved eye-spotpatterns on their wings to help ward off predators.Scaife (1976) reports a study examining how eye-spotpatterns affect the behavior of birds. In the study, thebirds were tested in a box with two chambers andwere free to move from one chamber to another. Inone chamber, two large eye-spots were painted onone wall. The other chamber had plain walls. Theresearcher recorded the amount of time each birdspent in the plain chamber during a 60-minute session.Suppose the study produced a mean of M = 34.5 minutes on the plain chamber with SS = 210 for a sample of n = 15 birds. (Note: If the eye spots have no effect,then the birds should spend an average of μ = 30minutes in each chamber.)a. Is this sample sufficient to conclude that the eyespots have a significant influence on the birds’behavior? Use a two-tailed test with α = .05.b. Compute the…

The majority of clothing retailers use mannequins to display their merchandise, with approximately one-third displaying mannequins with a head and two-thirds displaying mannequins without a head. Researchers recruited 126 female participants and assigned them to one of the two mannequin styles (head/headless). Participants were.asked to imagine that they wanted to buy a new dress and told that they had gone to a named store to make their purchase. They then viewed the dress displayed on a mannequin (head or headless) and asked whether they would buy the dress. Of the 53 participants viewing the dress displayed on a mannequin with a head, 18 indicated they would buy the dress, while only 10 of the 53 participants viewing the headless mannequin indicated they would buy the dress. Assuming the conditions are met, calculate the test statistic (Enter the test statistic rounded to two decimal places)

Many young men in North America and Europe (but not in Asia) tend to think they need more muscle to be attractive. One study presented 200 young American men with 100 images of men with various levels of muscle. Researchers measure level of muscle in kilograms per square meter (??/?2) of fat‑free body mass. Typical young men have about 20 ??/?2 . Each subject chose two images, one that represented his own level of body muscle and one that he thought represented “what women prefer.” The mean gap between self‑image and “what women prefer” was 2.35 ??/?2 . Suppose that the “muscle gap” in the population of all young men has a Normal distribution with standard deviation 2.5 ??/?2 . Give a 90% confidence interval for the mean amount of muscle young men think they should add to be attractive to women. (Enter your answers rounded to four decimal places.) lower limit=                     upper limit=