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The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to?138?±?19?pounds?(μ?±?σ).?Suppose we select a sample of 100 children?(n?= 100)to test whether children in this population are gaining weight at a 0.05 level of significance.What are the null and alternative hypotheses?H0:?μ?= 138H1:?μ?≠?138H0:?μ?= 138H1:?μ?> 138????H0:?μ?< 138H1:?μ?= 138H0:?μ?= 138H1:?μ?< 138What is the critical value for this test?What is the mean of the sampling distribution?What is the standard error of the mean for the sampling distribution?A cheerleading squad received a mean rating (out of 100 possible points) of?75?±?9?(μ?±?σ)?in competitions over the previous three seasons. The same cheerleading squad performed in?16?local competitions this season with a mean rating equal to?77?in competitions. Suppose we conduct a one-independent sample?z-test to determine whether mean ratings increased this season (compared to the previous three seasons) at a 0.05 level of significance.State the value of the test statistic. (Round your answer to two decimal places.)Compute effect size using Cohen's?d. (Round your answer to two decimal places.)State the total degrees of freedom for the following?t-tests. (If you need to use?∞, enter INFINITY.)n?=?23?for a one-independent sample?t-testdf1?=?15,?n2?=?21 for a two-independent sample?t-testcritical value = 63.657 for a two-tailed test,?α?= 0.01A schoolteacher is concerned that her students watch more TV than the average American child. She reads that according to the American Academy of Pediatrics (AAP), the average American child watches 4 hours of TV per day?(μ?= 4.0 hours). She records the number of hours of TV each of her six students watch per day. The times (in hours) are?2.5,?5.3,?4.2,?2.6,?4.6, and?4.8.Test the hypothesis that her students watch more TV than the average American child using a 0.05 level of significance and a one-independent sample?t-test. State the value of the test statistic. (Round your answer to three decimal places.)Compute effect size using estimated Cohen's?d. (Round your answer to two decimal places.)While researching lifestyle changes to improve heart health, you come across a research article reporting that the average American consumes about 2,700 calories per day?(μ?= 2,700). You come across another article that refutes this, stating that a sample of Americans consumed significantly less than this mean standard on average,?t(50) =?3.081, p?< 0.05 (η2?=?0.16). Assuming this test was a one-independent sample?t-test, what is the proportion of variance for this effect? (Round your answer to two decimal places) To demonstrate flavor aversion learning (that is, learning to dislike a flavor that is associated with becoming sick), researchers gave one group of laboratory rats an injection of lithium chloride immediately following consumption of saccharin-flavored water. Lithium chloride makes rats feel sick. A second control group was not made sick after drinking the flavored water. The next day, both groups were allowed to drink saccharin-flavored water. The amounts consumed (in milliliters) for both groups during this test are given below.Amount Consumedby Rats That WereMade Sick (n?= 4)Amount Consumedby Control Rats(n?= 4)5831118412Test whether or not consumption of saccharin-flavored water differed between groups using a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.)Compute effect size using eta-squared (η2). (Round your answer to two decimal places.) ................
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