1) Suppose the annual income of all British Columbian adults had an average of $35,000 and a standard deviation of $14,000. A random sample of 49 British Columbian adults was selected and they were asked about their annual income. Note that income has a right-skewed distribution.

a) Provide a description of the statistic of interest. [2 marks]

b) Identify the sampling distribution of the above statistic. [4 marks]

Note: Make sure you understand checking conditions is part of the procedure.

c) What the probability that the average annual income (of the 49 randomly selected British Columbian adults) is bigger than $38,500? [2 marks]

2) One way to know the efficiency of international airports is to measure the percentage of flights that leave the airport on time on a daily basis. From a random sample of 100 days, it was found that an average of 81.5% of flights leave YVR (Vancouver International Airport) on time and a standard deviation of 4.5%. From past experience, it is known that the percentage of flights that leave YVR on time has a Normal distribution.

a) Provide a description of the parameter of interest in this study. [2 marks]

b) Construct a 98% confidence interval of the parameter in part (a). [3 marks]

3) At Western University, the average scholarship examination scores for freshman applications has been 900. Every year, the assistant dean uses a sample of applications to determine whether the average examination score for the new freshman applications is different from 900. A random sample of 200 applications was drawn and the average score was found to be 935 and a standard deviation of 180. Historically, it is known that the score has a Normal distribution.

a) Identify the parameter of interest. [2 marks]

b) Set up the null hypothesis and the alternative hypothesis. [2 marks]

c) Calculate the test statistic and find the p-value [2 marks]

d) Draw a conclusion so that the Dean could understand. Use 5% significance level. [2 marks

4) A local pizza joint has recently hired additional drivers and claims that its average delivery time for orders is under 45 minutes. A random sample of 36 customer deliveries was examined and the average delivery time was found to be 42.3 minutes with a standard deviation of 11.6 minutes. The delivery time generally follows a Normal distribution.

a) Identify the parameter of interest. [2 marks]

b) Set up the null hypothesis and the alternative hypothesis. [2 marks]

c) Calculate the test statistic and find the p-value [2 marks]

d) Draw an appropriate conclusion using 5% significance level. [2 marks]

5) Trying to avoid over- or under-allocating labour hours in a particular moving job, the manager of a moving company would like to develop a better method of predicting labour hours (Hours; measured in hours) by using the size of the apartment (Feet; measured in cubic feet) moved. A random sample of 36 moves in the past year was randomly selected in the borough of Manhattan in New York City.

a) Use Excel to provide a scatterplot. [2 marks]

b) Use Excel to produce a Regression output. [2 marks]

c) Can we conclude that there is a significant correlation between the moving hour and size of all moves in Manhattan? Make sure you use the three-step process and an appropriate decision point to answer this question. [2+1+2 marks]

d) Write down the least square regression line. [2 marks]

e) Provide an interpretation of the slope estimate. [2 marks]

f) Provide an interval estimation when the size of the move is 900 square feet, with 95% confidence level. [3 marks]

6) The Titanic data set provides the information of four key categorical attributes for each of the 2201 people on board the Titanic when it struck an iceberg and sank. The two categorical variables of interest are Class (Class; First class, Second class, Third class, or Crew Member), and if they survived the sink (Survived; yes or no). The 2-statistic was found to be 190.4. Can we conclude that different social classes have different survival rates? Make sure you use the three-step process and an appropriate decision point to answer this question. [2+1+2 marks]