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d) Does the study show that computer games are a likely cause of rickets?Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls upon the skin, is essential for strong, healthy bones. The bone disease rickets was largely eliminated during the 1950s, but now there is concern that a generation of children more likely to watch TV or play computer games than spend time outdoors is at increased risk. A recent study of 3000 children randomly selected found 19% of them deficient in vitamin D. Complete parts a through d. a) Construct a 98% confidence interval for the true proportion of children who are deficient in vitamin D. Select the correct choice below and fill in any answer boxes within your choice. O A. (Round to three decimal places as needed.) O B. The conditions of a confidence interval are not satisfied.A poll of 1037 U.S. adults split the sample into four age groups: ages 18-29, 30-49, 50-64, and 65+. In the youngest age group, 61% said that they thought the U.S. was ready for a woman president, as opposed to 36% who said "no, the country was not ready" (3% were undecided). The sample included 259 18- to 29-year olds. a) Do you expect the 99% confidence interval for the true proportion of all 18-to 29-year olds who think the U.S. is ready for a woman president to be wider or narrower than the 99% confidence interval for the true proportion of all U.S. adults? b) Construct a 99% confidence interval for the true proportion of all 18- to 29-year olds who believe the U.S. is ready for a woman president.A company manufacturing CDs is working on a new technology. A random sample of ?60 Internet users were asked: 'As you may know, some l(ZDs are being manufactured so that you can only make one copy of the CD after you purchase it. Would you buy a CD with this technology, or would you refuse to buy it even if it was one you would normally buy?' Of these users, 69% responded that they would buy the CD. Complete parts a and b below. at Create a 90% condence interval tor this percentage. { |%. |%) {Round to three decimal places as needed. Use ascending order.) b) If the company wants to cut the margin of error in half, how many users must they survey?A very large study showed that aspirin reduced the rate of first heart attacks by 44%. A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. What is the null hypothesis the company will use? . . . Let p represent the reduction in the rate of first heart attacks from the new drug. Choose the correct answer below. O A. Ho: P > 0.44 O B. Ho: p#0.44 O C. Ho: P= 0.44 O D. Ho: P 0.4 at a = 0.01 c) Ho: H = 40 vs. HA: p # 40 at a = 0.01; n= 46 d) Ho: p = 0.7 vs. HA: p > 0.7 at a = 0.05; n =335 e) Ho: p= 50 vs. HA: u 18. A sample of size 16 results in a sample mean of 18.5 and a sample standard deviation of 2.3. a) What is the standard error of the mean? b) What is the critical value of t* for a 90% confidence interval? c) Construct a 90% confidence interval for u. d) Based on the confidence interval, at a = 0.05 can you reject Ho? Explain.Suppose that you are testing the hypotheses H: = 90 vs. HA: #90. A sample of size 51 results in a sample mean of 85 and a sample standard deviation of 1.4. a) What is the standard error of the mean? b) What is the critical value of t* for a 99% confidence interval? c) Construct a 99% confidence interval for j. d) Based on the confidence interval, at a = 0.010 can you reject H,? Explain.A Statistics professor has observed that for several years students score an average of 117 points out of 150 on the semester exam. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting that it will increase students' scores. The software is expensive, and the salesman offers to let the professor use it for a semester to see if the scores on the final exam increase significantly. The professor will have to pay for the software only if he chooses to continue using it. In the trial course that used this software, 241 students scored an average of 120 points on the final with a standard deviation of 8.7 points. Complete parts a) and b) below. a) Should the professor spend the money for this software? Support this recommendation with an appropriate test. Use a = 0.05. What are the null and alternative hypotheses? Ho HAb) Does this improvement seem to be practically significant?b) To be sure that the method was successful, the research department popped 8 more bags of popcorn (selected at random) at this setting. All were of high quality, with the percentages of unpopped kernels being 6.7, 12.9, 10.6, 7, 7.1, 3.1, 2.0, and 4.8. [ Does this provide evidence that they met their goal of an average of fewer than 11% unpopped kernels? Assume a = 0.05