4. (10 points) A computer scientist is investigating the usefulness of two different design languages in improving programming tasks. Twelve expert programmers who are familiar with both languages are asked to code a standard function in both languages and the time (in minutes) is recorded. The data follow: Time Programmer Design Language 1 Design Language 2 1 17 18 16 14 3 21 19 4 14 11 5 BT 23 6 24 21 7 16 10 8 14 13 9 21 19 10 23 24 11 13 15 12 18 20 Find a 95% confidence interval on the difference in mean coding times. Is there any indication that one design language is preferable?5. A random sample of 500 adult residents of Maricopa County indicated that 385 were in favor of increasing the highway speed limit to 75 mph, and another sample of 400 adult residents of Pima County indicated that 267 were in favor of the increased speed limit. a. (5 points] Do these data indicate that there is a difference in the support for increasing the speed limit for the residents of the two counties? Use Cl. = 0.05. What is the P-value for this test? b. Suppose that 331 = 0.75 and p2 = 0.65 . With the sample sizes given here, what is the power of the test for this two-sided alternate? c. Suppose that 391 = 0.75 and p2 = 0.65 . Determine the sample size needed to detect this difference with a probability of at least 0.9