# Chapter 1 HW STAT 380

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Stat 380: Chapter 1 Homework Summer 2023 _____________________________________________________________________________________________ Please complete each question and submit a printed/written copy by the end of class on Thursday (07/13/2023) 1. For each of the following situations, discuss the nature of the population of interest, the variable of interest, and the parameter of interest. a. A city engineer wants to estimate the average weekly water consumption for single- family dwelling units in the city. Population of Interest : Single-family Variable of interest : The weekly water consumption of a single-family (quantitative) Parameter of interest: Average of all single-family water consumption dwelling unit in the city in a week b. A medical scientist wants to estimate the average length of time until the recurrence of a certain disease. Population of Interest: People who has the disease Variable of interest: length of time period (Quan) Parameter of interest : Average of length of time until the recurrence of a certain disease c. An electrical engineer wants to determine whether the average lifetime of transistors of a certain type is greater than 500 hours. Population of Interest: Transistors Variable of interest: lifetime of transistors. (quantitative) Parameter of interest: Average lifetime of transistors of a certain type 2. To estimate the proportion of Americans who would be interested in a new type of ice skate, a random sample of 1500 Minnesotans are asked about their interest in the product. a. What is the population of interest? Americans b. What is the parameter of interest? Proportion interested in ice skating c. What is the sample? 1500 Minnesotans d. Will the statistic under- or over-estimate the parameter of interest? Explain. Overestimate because we are only looking at Minnesotans and no other states as well. Also because Minnesotans they have a lot of snow.
Stat 380: Chapter 1 Homework Summer 2023 _____________________________________________________________________________________________ 3. Here are the annual numbers of deaths from tornadoes in the United States from 1990 through 2000 (Source, NOAA): 53, 39, 39, 33, 69, 30, 25, 67, 130, 94, 40. 25, 30, 33, 39, 39, 40 , 53, 67, 69, 94, 130 Find the following statistics: a. Mean: 53 + 39 + 39 + 33 + 69 + 30 + 25 + 67 + 130 + 94 + 4 0 11 = 56.27 b. Median: 40 c. Range: 130-25 = 105 d. Variance xi ¿ ¿ ¿ 2 ¿ ¿ ¿¿ ¿ ( 53 56.27 ) 2 + ( 39 56.27 ) 2 + ( 39 56.27 ) 2 + ( 33 56.27 ) 2 + ( 69 56.27 ) 2 + ( 30 56.27 ) 2 + ( 25 56.27 ) 2 + ( 67 56. 11 1 = 1021.82 e. standard deviation= 1021.82 = 31.97 4. You are interested in finding out how much time a middle school student spends per week on their homework, on average. You select at random 6 middle school students in Lincoln and record their age, standing, and the time they spend per week, on average. Read all parts first. Age (years) Standing Time (per week) 12 Senior 10 13 Senior 3 14 Junior 4 16 Junior 5 13 Senior 5 13 Senior 4 a. Describe the sample (mean/std dev/median of age and time, proportion of senior-junior and any other relevant information). Limit to one paragraph.
Stat 380: Chapter 1 Homework Summer 2023 _____________________________________________________________________________________________ The study objective is trying to find the average time a middle school spends on his homework. Random Sample of 6 middle school students was conducted where age, stand and times per week spent was recorded. Mean of time per week is 5.17. The median is 4.5. b. Use statistical notation to correctly represent the calculated mean and standard deviation mentioned in part (a). Sample Mean: 3 + 4 + 4 + 5 + 5 + 10 6 = 5.17 Sample Variance = xi ¿ ¿ ¿ 2 ¿ ¿ ¿ ¿ ( 3 5.17 ) 2 + ( 4 5.17 ) 2 + ( 4 5.17 ) 2 + ( 5 5.17 ) 2 + ( 5 5.17 ) 2 + ( 10 5.17 ) 2 6 1 = 6.17 s= 6.17 Sample SD = 2.48 c. Identify any outliers. The outlier is the 12-year-old student that study 10 per week. d. Exclude the observations that correspond to the outliers from your data. What is the average time that students spend on their homework weekly now? 3 + 4 + 4 + 5 + 5 5 = 4.2 5. Consider the data: {7, 1, 9, 12, 5, 10}. Compute the sample variance and sample standard deviation. Assign correct notation. 1,5,7,9,10,12 Mean: (1+5+7+9+10+12)/6 = 7.33