Topics: - Estimation of the mean and proportion and Hypothesis Testing

Question 1   

a) You, the district sales manager for a fast-food company prefer to compare sales performance in terms of standardized values. You recently hired a new analyst, and you decided to demonstrate to her how to standardize the value x = 15 given  = 9 and  = 5. Show the working you demonstrated to the new analyst.

b) Based on your knowledge on the z statistic and the t statistic, a confidence interval inappropriately using a z-statistic instead of the tstatistic will give a wider, or narrower interval? Why?

c) The manager of John’s supermarket received complaints from Cashiers at the supermarket that many customers who used the express checkout lane have more than the stipulated number of items for the lane. The express check-out lanes are limited to customers purchasing 10 or fewer items. A recently taken random sample of 25 customers entering express lanes at this supermarket found that 14 of them had more than 10 items. 

i. (i) Construct a 95% confidence interval for the percentage of all customers at this supermarket who enter express lanes with more than 10 items

ii. (ii) Give a complete interpretation for the 99% confidence interval from part (i)