1. The standard IQ test has a mean of 96 and a standard deviation of 14. We want to be 99% certain that we are within 4 IQ points of the true mean. Determine the required sample size.2. In 1908, W.S. Gosset published the article “The Probable Error of a Mean” (Biometrika, Vol. 6, pp. 1-25). In this pioneeringpaper, written under the pseudonym “Student,” Gosset introduced what later became known as Student’s t-distribution. Gosset used the following data set, which gives the additional sleep in hours obtained by a sample of 10 patients using laevohysocyamine hydrobromide (hereinafter referred to as “the drug”). 1.9 0.8 1.1 0.1 -0.1 4.4 5.5 1.6 4.6 3.4a. Create a 95% confidence interval for the additional sleep that would be obtained on average for all people using the drug. Briefly explain the process that you used and why.b. Give an interpretation of the confidence interval that you found in part a. That is, what does it mean? c. Make an inference: Was the drug effective in increasing sleep? Explain your reasoning.ReferenceWeiss, N., (2008) Elementary statistics, (7th Ed.). Boston, MA: Pearson.
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