(a) A performance analyst simulated a computer system a total of 10 times, each simulation run independent of all the others. She calculated and recorded the sample means for system response time from each of the 10 runs, coming up with the following data (measured in seconds): 6,15,17,8,9,7,10,25,5,11 i) What is the confidence interval with a 95% confidence level for the mean response time? If measurements from the real system gave a mean figure of 12 seconds for the response time, Comment on the statistical validity of the confidence intervals constructed in part (i). ii)

Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain. (Let 1 = Linda's rats, 2 = Tuan's rats and 3 = Javier's rats.) Weights of Student Lab Rats Linda's rats Tuan's rats Javier's rats 43.0 46.9 51.1 38.5 40.1 40.4 40.7 38.4 37.1 45.8 45.7 44.8 37.8 43.6 47.7 Part (a) State the null hypothesis. H0: ?1 = ?2 = ?3 H0: At least two of the group means ?1, ?2, ?3 are not equal.      Part (b) State the alternative hypothesis. Ha: ?1 = ?2 = ?3 Ha: At least two of the group means ?1, ?2, ?3 are not equal.      Part (c) Enter an exact number as an…

A random sample of high school students is used to estimate the mean time all high school students study for Algebra II tests. A 99% confidence interval based on this sample is: 1.7 hours to 3.1 hours.  What is the sample mean?

An investigation is performed to evaluate two new experimental treatments for allergies. 18 subjects who suffer from allergies are enrolled in the study and randomly assigned to one of three treatments: Control Group, Experimental Treatment 1, or Experimental Treatment 2. Each subject is instructed to take the assigned treatment, and symptoms of allergies are recorded on a scale of 1 to 20, with higher scores indicating worse symptoms. The data is summarized in the table below: SBP Std. Deviation Group Mean Control Treatment 6. 16.17 2.483 Experimental Treatment 1 6. 11.33 1.966 Experimental Treatment 6. 3.83 1.472 Total 18 10.44 5.554 Use this data to complete an ANOVA table to test for a significant difference in the means of each of the groups. Round all answers to the third decimal point.