Statistics Assignment: Case Analysis Based On Business Decision Making
Question
Task:
You must write a statistics assignment addressing the following tasks:
Question 1
Car buyers in the city of Newcastle were asked by a car dealer to rate their level of satisfaction with the service that they received. The four possible ratings were: Excellent (E), Good (G), Satisfactory (S) and Unsatisfactory (U). Data showing the level ofsatisfaction with the service for December 2019, is provided in the file Question1.xlsx.Column A contains the level of satisfaction scores.
(i) What type of variable is “level ofsatisfaction” (Continuous, Discrete, Ordinal or Nominal) Be sure to justify your answer.
(ii) Name the appropriate graphical display to use to display ‘level ofsatisfaction’, based on the variable type you identified in part (i).
(iii) Use Excel to create the appropriate graph to display the provided data.
(iv) Comment on the key aspectsfrom this graph.
Question 2
The University of Newcastle marketing services are interested in mobile usage technology. A study was undertaken in which a random sample of students enrolled at the University of Newcastle in 2019 and 2020 were invited to participate in a project about the daily usage of smartphones. There were 50 randomly selected students in 2019 and 50 randomly selected students in 2020 who participated in the study. Data is provided in the Excel file Question2.xlsx. Columns A contains student smartphone daily usage in 2019 and Column B contains student smartphone daily usage in 2020 (minutes per day).
(i) Use Excel to construct a histogram of student smartphone daily usage in 2019. How would you describe the distribution, including the shape Include a histogram with your response.
(ii) Use Excel to construct a histogram of student smartphone daily usage in 2020. How would you describe the shape Include a histogram with your response.
(iii) Use Excel to find the mean, median, standard deviation and interquartile ranges of student smartphone daily usage in 2019. Repeat for the smartphone daily usage in 2020.
(iv) Using the information from parts (i)-(ii), give a brief statement comparing smartphone daily usage in 2019 with smartphone daily usage in 2020.
(v) Explain, using support from a hypothesis test, if the average smartphone daily usage in 2019 differs from the average smartphone daily usage in 2020. Perform the hypothesis test at the 5% significance level. Assume that data in 2019 and 2020 were taken from different students.
Be sure to include the following in your answer:
the null and alternative hypotheses
the p-value
conclusion
(Hint): Research Question: Wasthe average smartphone usage the same in 2019 and 2020
Question 3
The data was collected by the marketing research department randomly selecting 100 Mazda cars model and transmission preferencesin the city of Newcastle. A study was conducted to investigate the type/s of models and transmission preferences from the Mazda car dealers. Use Figure 1 to answer the following probability questions (i) – (iv).
(i) What is the probability that a randomly selected customer bought the SUV car
(ii) What is the probability that a randomly selected customer bought the SUV and Automatic car?
(iii) What is the probability that a randomly selected customer bought the Hatch or Automatic car?
(iv) What is the probability that a randomly selected customer bought the Sedan car given Automatic car?
(v) Consider the 20 Automatic cars who prefer the Sedan cars from observed frequencies. For this cell of the table above (Figure 3): calculate the expected count.
(vi) Conduct an appropriate formal hypothesis test at the 5% significance level to see if there is a statistically significant relationship between preferences for the type/s of Mazda cars model and transmission preferences. Use P-value approach to answer the research question. Use Figures 1-3 to answer the research question.
Answer
Answer 1
i) The level of satisfaction is continuous variable as the ratings given by the customers is considered to be continued till the time of the rating. The words ofSmarandache (2021) considered herein statistics assignmentconfirmed that the continuous variable helps in maintaining a graphical representation and have proper outcome.
ii) The most appropriate graph graphical display to use while giving an analysis of the level of satisfaction is bar graph. The bar graph of the data is given below as well as in the excel sheet.
iii)
iv) From the above graph it can be confirmed that majority of the respondents give excellent ratings and only 6 out of 50 respondents gave and satisfactory rating. Therefore from the graphical representation it can be confirmed that the car dealers in the city of Newcastle have created proper level of satisfaction among the car buyers.
Answer 2
i)
iv) From the information collected from the histogram created in the excel, it can be explained that almost 18/ out of 50 respondents use mobile phone on an average of 159.7 to 177.7 in 2019 whereas more than 10 to 15 respondents use mobile phone while having the usage of 154.7 to 171.7 in 2020. From the graphical representation it can be confirmed that the mobile usage increased in 2020 because the major number of respondents using mobile phone increases along with the increase of the usage.. In simple terms, in 2019 majority of the people had an average usage of 159.7 to 177.7 which increased to 171.7 to 188.7 in 2020.
v) H0: There exist same average smartphone usage in 2019 and 2020. (null)
H1: the average smartphone usage in 2019 is less compare to 2020. (alternative)
p-value for H0: 0.97>0.05
p-value for H1: 0.701>0.05
From the null and alternative hypothesis and the P value for both the hypotheses, it can be concluded that both the P values are more than 5% significant level. Therefore the null value is rejected and the alternative hypothesis is justified. From the analysis it can be confirmed that the P value for alternative hypothesis is less than the P value for null hypothesis which indicates that the average usage for mobile phone in 2020 is more compare to the mobile usage in 2019.
Answer 3
i) 57/100= 0.57
ii) 35/100=0.35
iii) (20/100)+ (73/100)= 0.93
iv) 20/100= 0.2
v) 23-6.21= 16.79
vi) H0: There is statistically significant relationship between the preferences of the Mazda car models and the transmission preference.
H1: The preferences of the Mazda car models and the transmission preference are different
p-value: 0.14
Since the P value is less than the significant value, therefore the null hypothesis is rejected. It can be concluded that there exist no significant link between the types of mass the car model and the transmission preference. Therefore it can we confirm that the preferences of the customers I’m not directly influenced by their transmission Preferences which might be beneficial for the company to work on the strategies added in the transmission preferences.
Reference list
Smarandache, F., (2021). Plithogenic Probability & Statistics are generalizations of MultiVariate Probability & Statistics. Statistics assignmentNeutrosophic Sets and Systems, 43, pp.280-289. https://books.google.co.in/books?hl=en&lr=&id=UlxCEAAAQBAJ&oi=fnd&pg=PA280&dq=probability+and+statistics&ots=zLNYKfrcAm&sig=_ubJ4WMr-nQMkuV6x2EtHC8gfpA&redir_esc=y#v=onepage&q=probability%20and%20statistics&f=false
