Take Home Assignment (Topic 7) Estimation Show all workings. Question 1 (a) English-speaking student The university education committee wants to estimate the proportion of people who speaks English in the undergraduate classes. A survey of 250 students revealed 50 speaking English. Construct by hand a 95% confidence interval for the proportion of English-speaking students. (b) If the company wanted to estimate the sample proportion to within 3% of the population proportion at the confidence level of 95%, what sample size would be necessary assuming no prior estimate of the proportion is known (Hint: p=0.5 if no prior estimate of the proportion is known.)? Question 2 Production Rates A manufacturing company wishes to estimate the number of items that its workforce can produce on average each hour now that they have a new machine. The factory examined the records for a random sample of 8 hours over the past month. The hourly production rates for these 8 hours were: 158 (a) 162 171 164 194 152 169 176 Calculate by hand and interpret the 95 percent confidence interval for the average number of items produced per hour. (b) What assumption did you make for the population in order to answer part (a)? Note: Submit THA online via Blackboard-assessment-submit THA (Topic 7) here. Please make sure your submission complies with the following requirements: 1. Single file (either PDF or Word file) submission for the THAs into the right folder (Topic 7). 2. If you have graphs included, PDF file is preferable as the graphs sometimes are not placed properly in the word file. 3. For the marking purpose, your submission file has to be accessible and clear enough. Due: Sep 17 (Sat) 11:59pm (Week 7) 1