Suppose that a group of researchers is planning to test a new weight loss supplement. They have selected a random sample of 50 people who are trying to lose weight and plan to measure the amount of weight lost after one month of using the supplement. Assume that the researchers know from prior experiments that the standard deviation of weight lost in one month, o, is 1.5 lb. To show that the supplement is effective, they plan to use a one-sample z-test of Ho: =0 lb against H1: µ > 0 lb, where u is the mean amount of weight lost in one month. They have also determined that, for a test with a significance level of 0.01, the power of the test is 0.8348 if the mean amount of weight lost is actually 0.7 lb. What is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.7 lb or more? Give your answer as a percentage, precise to two decimal places.

In a random sample of 75 eighth grade students scores on a national mathematics assessment test has a mean score of 266. The test result prompts a state school administration to declare that the mean score for the stated eighth graders on this exam is more than 260. Assume the population standard deviation is 34. At a=0.09, is there enough evidence to support the administrations claim? Write the claim mathematically and identify Ho and Ha Find the standardized test statistic z, and its corresponding area

Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was 4.5 days, and the standard deviation of overall duration of symptoms was 1.6 days. For the placebo group, the mean overall duration of symptoms was 8 days, and the standard deviation was 1.8 days. (a) Calculate a 95% confidence interval for the mean overall duration of symptoms in a population of individuals like those who used the zinc lozenges. (Round your answers to two decimal places.)to days(b) Calculate a 95% confidence interval for the mean overall duration of symptoms in a population of individuals like those who used the placebo lozenges. (Round your answers to two decimal places.)to days(c) On the basis of the intervals computed in parts (a) and…

Scores on a certain "IQ" test for 18-25 year olds are normally distributed. A researcher believes that the average IQ score for students at a certain NJ college is less than 110 points, and so wants to test this hypothesis. The researcher obtain a SRS of 45 student IQ scores from school records and found the mean of the 45 results was 108 with a sample standard deviation of 21. The level of significance (alpha) used for this problem is 0.05. What is the appropriate test statistic (Student must complete by showing by formula using the ap- propriate values in that formula "showing work" and the final answer and appropriate label)? O T test score = (108-110)/(21/sqrt(45)) = -.639 T test score (108-110)/(21/sqrt(45)) = .639 %3D OT test score = (110-108)/(21/sqrt(45)) = .639 %3D T test score (108-110)/(45/sqrt(21)) =-.2037 %3D 素