i want to know these 5 questions Q1 to Q5

OF EB Mi | W| As | Ch |Gar | Go S Sy G Ho & GO T SE & Go X Da| EX | BL| Cli|J CC|PQ Se |9 as | ch | ch |m Cc |* Hc| (4 . C a www-library-In-edu-hk.lingnan.idm.oclc.org/sites/default/files/restrict_file/examination/3y/2122/BUS1102_21221.pdf Update : E BUS1102_21221.pdf 2 / 18 1 - 100% + Student number: Part I Analysis Questions You are required to answer ALL questions Question 1: [10 Marks] In NL University, the height of students has a mean of 162cm and a standard deviation of 19cm. 70 students are randomly selected. With reference to this sample of 70 students, what is the standard deviation of the sampling distribution of the sample mean of heights? [2 marks] b) What is the probability that the sample mean of heights will be less than 169cm? [4 marks] c) What is the probability that the sample mean of heights will more than 185cm? [4 marks] Answer:OF B & Mi | W | As @ Ch | G ar | Go S Sy G Ho & GO T SE & Go X Da | Ex | BL| Cli|J CC|PQ Se | as | ch | ch|T Cc * Hc| (4 . C a www-library-In-edu-hk.lingnan.idm.oclc.org/sites/default/files/restrict_file/examination/3y/2122/BUS1102_21221.pdf G V A 3 Ing Update : E BUS1102_21221.pdf 3 / 18 100% Question 2 [15 marks] The staff union wants to estimate the amount of overtime works (OT) per month of employees in a very large company. Assume the population is normally distributed and based on a previous study, the population standard deviation is 12 hours per month. A survey will be conducted to collect the amount of OT works per month in hours. a) How many respondents should the staff union select if they want to estimate the mean hours of OT works per month within 2 hours with 99% confidence? [5 marks] b) Due to resource limitations, the staff union decided to take a sample of 200 respondents. This yields a mean OT works of 45 hours per month. Construct a 99% confidence interval of the mean of this OT works per month for this very large company. [5 marks] c) The staff union also wants to estimate the proportion of staff who needs to have OT works in a month. In this sample of 200 respondents, 15% of the respondents indicated that they need to work overtime in a month. Construct a 99% confidence interval of the proportion of respondents who need to work OT in a month. [5 marks] Answer:OF EB Mi | W| As | Ch |Gar | Go |S Sy G Ho & GO T SE & Go X Da| EX| BL| Cli|J CC|PQ Se |9 as | ch | ch |In Cc| Hc| (4 . C a www-library-In-edu-hk.lingnan.idm.oclc.org/sites/default/files/restrict_file/examination/3y/2122/BUS1102_21221.pdf Update : E BUS1102_21221.pdf 5 / 18 100% + Question 3: [16 marks] A recent survey reported that the average height of ABC students was 169cm. You suspect that the real mean should be lower according to your observations. In order to verify the accuracy of this survey, you randomly selected 20 students. Their heights are listed below: 165 172 159 170 176 186 150 165 162 170 156 155 163 158 153 158 162 178 164 160 Based on the collected 20 data and if you are willing to take a 5% risk of making a type I error, what conclusion will you make after you conduct a hypothesis test? Support your answer with reasons. Assuming the heights of ABC students are normally distributed). Answer:OF EB Mi | W| As @ Ch |G ar | Go|S Sy |G Ho & GO T SE & Go X Da| Ex | BL| Cli|J CC|PQ Se |9 as | ch | ch |T Cc |* Hc| (4 . C a www-library-In-edu-hk.lingnan.idm.oclc.org/sites/default/files/restrict_file/examination/3y/2122/BUS1102_21221.pdf Update : E BUS1102_21221.pdf 6 / 18 100% Question 4: [16 Marks] A pressure group has been monitoring the percentages of monthly donations to a charitable organization in HK. It is suspected that the percentage of monthly donations of donors who are in the age group of 35-45 years old has been dropping. Over the years, the percentage of donations generated from this age group has been 37%. A random sample of 200 donors of 35-45 years old was selected. It is found that the percentage of monthly donations for a charitable organization in this sample is 30%. Is there enough evidence to conclude that the percentage of monthly donations of 35-45 years old donors in HK has been decreasing? Assuming a 5% significance level is used. (The appropriate tables can be found in the appendix.) Answer:OF EB Mi | W| As @ Ch |G ar | Go S Sy G Ho & GO T SE & Go x Da| Ex | BL| Cli|J CC|PQ Se | as | ch | ch |T Cc |* Hc| (4 . C a www-library-In-edu-hk.lingnan.idm.oclc.org/sites/default/files/restrict_file/examination/3y/2122/BUS1102_21221.pdf G VA = Ing Update : E BUS1102_21221.pdf 7 / 18 100% + Question 5: [18 Marks] Background A large supermarket is interested in reducing the amount of time that a customer spends waiting to be served by a cashier. The supermarket manager is interested in the relationship between waiting time in minutes and the number of cashiers on duty. 13 customers were randomly selected with the data given below: The partial Excel output is generated below: Regression Statistics Multiple R R Square 0.62212 Adjusted R Square 0.587767 Standard Error 2.385754 Observations D ANOVA df Ss MS F Significance F Regression 1 C 103.0776 18.10978 0.001353 Residual 11 62.61005 5.691822 Total B 165.6877 Coefficients Standard t Stat P-value Error Intercept 4.43394 1.765315 3.176408 5.31E-06 Number ofcashier on duty -1.74118 0.409153 -4.25556 0.001353 (a) Fill in the blanks in the Summary Output: [4 marks] A B D (b) State the Regression Line in order to predict the waiting time using the number of cashiers on duty. [2 marks] (c) On a particular day, if there are 4 cashiers on duty, what will be the waiting time in minutes? [2 marks]OF EB Mi | W| As @ Ch |G ar | Go S Sy |G Ho & GO T SE & Go X Da| Ex | BL| Cli|J CC|PQ Se |9 as | ch | ch |T Cc |* Hc| (4 - C a www-library-In-edu-hk.lingnan.idm.oclc.org/sites/default/files/restrict_file/examination/3y/2122/BUS1102_21221.pdf G VA = Ing Update : E BUS1102_21221.pdf 8 / 18 1 - 100% + (d) State the coefficient of determination of this regression model and interpret it. [3 marks] (e) Using a 5% level of significance, test if the number of cashiers on duty is a factor influencing waiting time (minutes). [4 marks]OF EB Mi | W| As @ Ch |G ar | Go S Sy G Ho & GO T SE & Go X Da| EX | BL| Cli|J CC|PQ Se | as | ch | ch |T Cc |* Hc (4 . C a www-library-In-edu-hk.lingnan.idm.oclc.org/sites/default/files/restrict_file/examination/3y/2122/BUS1102_21221.pdf G VA = Ing Update : E BUS1102_21221.pdf 9 / 18 100% + (f) With reference to the Summary Output and your answer to (a)-E, discuss if the manager is having a good model to predict the waiting time using the number of cashiers on duty [3 marks]