Question 1 Explain the following concepts: 

(a) Parameter (1 marks) 

(b) Stratified random sampling (3 marks) 

(c) Descriptive statistics (3 marks) 

(d) Inferential statistics (3 marks) 

Question 2 

The following table displays data on height of students (measured in centimeters) in a Business Statistics class. The sample size consists of 30 randomly selected students for a particular class. 

Refer to table in question 2 in file

(a) Draw a histogram to depict the data above (5 marks) 

(b) Compute the mean (10 marks) 

(c) Calculate the variance and standard deviation (10 marks) 

(d) Calculate the coefficient of variation (5 marks) 

(e) Interpret the distribution of heights as shown in your histogram (5 marks) 

 Question 3

 Part 1: Two fair dice are rolled 

(a) Calculate the probability that two sixes will appear? (2 marks) 

(b) Calculate the probability of at least one six appearing? (5 marks) 

Part 2 

(a) A bank conducted a survey to estimate the proportion of its customers who would be interested in using a new app for mobile banking services. The bank found that 68 out of 150 customers are in favour of using the new app. Construct a 

(i) 95% confidence interval (10 marks) 

(ii) 90% confidence interval (10 marks)  

For the proportion of customers who are in favour of the new banking app 

 (b) A certain security system contains 12 parts. Suppose that the probability that each individual part will fail is 0.3 and that the parts fail independently of each other. Given that at least two of the parts have failed, compute the probability that at least three of the parts have failed? (8 marks) 

 Question 4 

(a) The mean lifetime of 200 mobile phones in a sample is 1,000 hours and their standard deviation is 130 hours. µ is the mean lifetime of all the mobile phones produced. Test the hypothesis that the sample comes from a population whose mean is 1,200 hours at 1% significance level? (10 marks) 

 (b) Consider a random sample of 20 observations. The sample variance is 30.5. Construct a 95% confidence interval for σ 2 (10 marks)