STAT Assignment 1

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School

Langara College *

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Course

1123

Subject

Statistics

Date

Feb 20, 2024

Type

pdf

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Uploaded by achirabhasingh

ACHIRABHA SINGH (100408568) 1 STAT 1123 ASSIGNMENT 1 1. An instructor would like to estimate the average commuting time (in minutes) that Langara students take to get to college from home. All Langara students were first grouped by schools (Arts, Business, Science & Technology, Humanities & Social Science, and Health), and then 50 students were randomly selected from each school to form the sample. (12 marks) a. Which sampling design was applied in this study? Briefly explain your choice. (3 marks) Stratified Sampling design was applied in this study to calculate the average commuting time in minutes, it takes for Langara students to get to college from home. The population i.e., all Langara students were divided into different groups ( strata's ) based on their school (Arts, Business, Science & Technology, Humanities & Social Science, and Health). And further 50 students were randomly selected from each group ( stratum ). b. Identify the population of interest in this study. (1 mark) All Langara Students is the population of interest in this study. c. Identify the sample in this study. Be specific. (1 mark) 50 randomly selected Langara students from each school (group) ( Arts, Business, Science & Technology, Humanities & Social Science, and Health ) is the sample in this study. d. What is the variable of interest being measured? Be sure to include the unit of measurement. (1 mark) The variable of interest being measured is the commute time it takes for 50 randomly selected Langara students (from each school) to get to college from home in minutes . e. Which scale of measurement is most appropriate to describe this variable? (1 mark) Interval scale of measurement if the most appropriate to describe this variable commute time ( since the value of the variable in the identified situation cannot be 0 ). f. Describe the parameter in this study. (1 mark) The average commuting time ( in minutes ) that 50 randomly selected Langara students (from each school) take to get to college from home is the parameter in this study. g. Suppose the average commuting time was found to be 45 minutes among those randomly selected Langara students. Is this value a parameter or a statistic? Briefly explain your choice. (2 marks) This value is to be considered as a statistic as it is obtained by using all the values in the sample that consists of r andom 50 Langara students selected from each school (Arts, Business, Science & Technology, Humanities & Social Science, and Health) ( stratum )

ACHIRABHA SINGH (100408568) 2 h. Which graph is most appropriate to summarize the above variable: bar graph or histogram? Briefly explain your choice. (2 marks) Since the average commuting time it takes for Langara students to commute to college from home in minutes in quantitative ( numerical data ). The graph that will be the most appropriate to summarize will be the histogram . Since the histogram displays classes of data , the time can be demonstrated as classes and simultaneously the number of students who fit in a class ( takes that much time to commute ) can be counted as the respective frequency (frequency distribution table) . 2. The Vancouver School Board wanted to investigate whether secondary school students have more homework to do now than in previous years. Eric Hamber Secondary School and Point Grey Secondary School were randomly selected and all teachers from these two schools were interviewed. (5 marks) a. Which sampling design was applied in this study? Briefly explain your choice. (3 marks) The sampling design applied in to investigate whether secondary school students have more homework to do now than in previous years is Cluster Sampling. As initially Eric Hamber Secondary School and Point Grey Secondary School are randomly selected i.e., the population is divided into clusters (secondary schools) and further these 2 clusters are selected as a whole i.e. all teachers from these two schools were interviewed. b. Briefly explain why this study is likely to have selection bias. (2 marks) This study to investigate whether secondary school students have more homework to do now than in previous years is likely to have selection bias because to draw out a comparison in the homework the sample size is too small because only 2 schools are selected leaving certain parts of the population completely secluded. The sample is not representative since only 2 secondary schools Eric Hamber Secondary School and Point Grey Secondary School are taken into consideration and the aim is to investigate the amount of homework in comparison to the previous year at secondary school . 3. A random sample of 30 Langara students was selected. The number of hours per day that they spend on social media are listed below. (7 marks) a. Which scale of measurement is most appropriate to describe the above data? (1 mark) Ratio scale of measurement is used to describe the number of hours per day spent by random 30 Langara students on social media. Since the data can have interval scale values and a meaningful 0 to represent the variable.

ACHIRABHA SINGH (100408568) 3 b. Draw a stem-and-leaf plot for the above data. Be sure to include the unit. (4 marks) Unit- 0.01 c. Describe the shape of the stem-and-leaf plot in the context of the question. (2 marks) The distribution of the number of hours 30 randomly selected Langara students spend on social media per day is right skewed . 4. Canada competed at the 2022 Winter Olympics. The final medal count is summarized below. (4 marks)

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ACHIRABHA SINGH (100408568) 4 a. Which scale of measurement is most appropriate to describe the data? (1 mark) Ordinal scale of measurement is the most appropriate since the final medal count of Canada at 2022 Winter Olympics is qualitative and ranked and no precision between the ranks exist. b. Find the percentage of gold medals. (1 mark) % of gold medals = [ frequency (gold medals)/ Sum of all frequency (sample size) ] * 100 Frequency of gold medals = 4 Sum of all frequencies (sample size) = 26 % of gold medals = (4 / 26) * 100 = 15.38% c. Which graph is most appropriate to summarize the data: bar graph or histogram? Briefly explain your choice. (2 marks) Since the final medal count of Canada in 2022 winter Olympics in qualitative ( ordinal data ). The graph that will be the most appropriate to summarize will be the bar graph . Since the bars (vertical / horizontal) displays qualitative data in this case gold, silver and bronze , the frequency can be demonstrated by their heights / lengths accordingly.

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