MS 5318 – Homework # 1
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MS 5318 – Homework # 1
Due: Friday, Feb 11, 2023.
Instructions:
• Submit Homework Assignments individually.
• This assignment contains multiple-choice, short-answer, and Excel questions. Each multiple-choice question has only one correct answer. For short-answer questions, you may receive partial credits by showing all work even if your final answer is incorrect.
1. (2 pts) The infant mortality rate is defined as the number of infant deaths per 1,000 live births. This rate is often used as an indicator of the level health in a country. The relative frequency (percentage) histogram shows the distribution of estimated infant death rates in 2012 for 222 countries.
(1.1) Use the histogram to estimate the interval containing the Median. (1 pt)
a. 0 to 10
b. 10 to 20
c. 20 to 30
d. 30 to 40
e. 40 to 50
(1.2) For this distribution, where is the mean located relative to the median? (1 pt)
a. The mean is to the left of the median.
b. The mean and the median should be almost the same.
c. The mean is to the right of the median.
d. This cannot be determined from the histogram.
2. (3 pts) A chemical plant is allowed to dispose a certain amount of waste water into a river. The Environmental Protection Agency (EPA) takes samples of the river water at several locations downstream from the plant. If the plant complies with the EPA regulations, the population mean amount of toxic particles in the water is μ=50 parts per million (ppm). Each day, the EPA selects 36 water samples and computes the average amount of toxic particles, and then uses this information to determine if they should conclude that the population mean amount of toxic particles is greater than 50 ppm. If so, the owner of the plant will be fined. Use the hypotheses Ho: μ≤50 ppm and Ha: μ>50 ppm. If the sample mean and sample standard deviation are 
= 52.3, S = 6.2. Determine whether the owner of the plant should be fined at the significance level a = 0.05.
3. (3 pts) iq.xlsx contains IQ scores of 60 persons.
Create a histogram for this data with the following requirements:
Use intervals: 80-89, 90-99,…,140-149 for the bars in the histogram. (1 pt)
Make sure there is no gap among the bars. Label x-axis “IQ Score,” y-axis “Frequency,” and title “Histogram.” (1 pt)
4. (4 pts) An experimenter conducted a blind taste test of lattes from Starbucks and McCafes. A sample of 33 customers tasted both lattes from unmarked cups and provided ratings on a -3 (=worst latte I’ve ever tasted) to +3 (=best latte I’ve ever tasted) scale. These data are in
Latte.xlsx. Use the hypotheses H0: μMcCafe ≤ μ Starbucks, Ha : μMcCafe > μ Starbucks .
(4.1) Select and run the correct t-procedure in Excel. Include the Excel t-test output in your submission, not the original data. (2 pts)
(4.2) What is the p-value of the test? What is the conclusion of the test at a = 10%. (2 pts)
5. (4 pts) The Nationals General Manager is concerned that his club may not be paying competitive salaries. He has asked you to compare Nationals’ salaries with salaries of players for the closest team in the National League East, the Phillies. He suspects that the Phillies may win more games because they are attracting better players with higher salary offers. Data are in Nationals.xlsx. Use the hypotheses H0: μ Phillies ≤ μnationals; Ha : μ Phillies > μnationals .
(5.1) Select and run the appropriate t-procedure in Excel. Include the Excel t-test output in your submission, not the original data. (2 pts)
(5.2) To determine if Phillies is paying significantly higher salaries than Nationals, what is the p- value of the test? What’s your conclusion based on the test? Use a = 1%. (2 pts)
6. (4 pts) The average number of hours of sleep that US college students get is known to be Normally distributed, with μ = 7.02 hours and σ = 1.15 hours.
(6.1) What proportion of students get less than 5 hours of sleep per night on the average? (1 pt) (6.2) Sam gets an average of 8.3 hours of sleep. What is Sam’s percentile score? (2 pts)
(6.3) What is your percentile score? (1 pt)
2023-02-19