PLEASE SOLVE IN PROPER FORMAT AND SHOW PROPER WORKINGS

1. Suppose that you are investigating the number of minutes required to complete a 40 multiple choice questions UAES 200 exam. From previous tests, the standard deviation of the minutes spent on the exam was 10 minutes. You have randomly selected 36 students who have taken the course in the fall 2021 and spring 2022 semesters, and the average period spent is recorded as 28 minutes.

Required?

(a) Discuss and construct a 99% confidence interval for the mean number of minutes required to complete exam.(Points = 15%)

(b) Suppose that the instructor allocates 40 minutes for the exam. Discuss whether the instructor should continue allocating 40 minutes of time for the exam. (Points = 10%)

2. The Samsung Company produces more than 100 million smartphones in a year. The company aims to lower the proportion of defective smartphones to 1%. In its annual quality investigation, the operations department of the company has taken a sample of 15,000 smartphones and found that 300 of them were defective.

Required?

(a) Discuss and compute the 95% confidence interval for the proportion of defective smartphones? (Points = 15%)

(b) Based on the estimated confidence interval, provide your conclusion on the company's goal to reduce the proportion of defective products to 1%. (Points = 10%)

3. Suppose that you are planning to open a bookshop in Ras Al Khaimah. Your random guess assumes that the majority of people who are between 25- 45 years old are interested to read books. You have surveyed 1,600 individuals and their response on whether they have read at least one non-academic book in the past 6 months is summarized as follows.

Gender	Read at least one non-academic book	Have not read any non-academic book	Total
Male	200	540	740
Female	320	540	860
Total	520	1,080	1,600

Required?

(a) Discuss and compute the 90% confidence interval for the proportion of males who have not read at least one book in the past 6 months? (Points = 15%)

(b) Discuss and compute the 99% confidence interval for the proportion of females among female respondents who have read at least one book in the past 6 months? (Points = 15%)

4. It has been reported that the average tuition fee per year for a Bachelor's Degree in Business in UAE colleges is 40,000 Dirhams. As a researcher, you want to test whether this claim is true. Suppose that you conduct a study of 9 randomly selected colleges and you find that the average tuition fee per year is 46,000 Dirhams with a sample standard deviation of 9000 Dirhams.

Required?

(a) Discuss and construct a 99% confidence interval for the average annual tuition fee for a Bachelor's Degree in Business in the UAE. (Points = 20%)