Emawk
03-04-2006, 08:55 PM
Hi, I'm stuck on a question and was wondering if you guys could help me. This is the problem I have a question about:
This question continues on to say that "A recent graduate of a business program believes that a survey of the university's students can apply the needed information. Accordingly, she organizes a survey that asks 500 students to keep track of the number of soft drinks they purchase on campus over the next 7 days. Perform the statistical analysis to extract the needed information from the data. Estimate with 95% confidence the parameter that is at the core of the decision problem. Use the estimate to compute estimates of the annual profit. Assume that Coke and Pepsi drinkers would be willing to buy either product in the absence of the first choice.
a. On the basis of maximizing profits from sales of soft drinks at the university, should Pepsi agree to the exclusivity agreement?
b. Write a report to the company's executives describing your analysis?"
The sample size is 500. I calculated it's mean to be exactly 1.316 and the standard deviation to be 1.114733. Because the population standard deviation in the question is not given, I used the confidence Interval Estimator of the population mean when the stadard deviation is unknown to find a range in which the population mean falls (to make an inference about the mean). The formula I used is xbar ± tα/2(s/√n).
Using the t-table (the t-value I used is 1.960), I calculated the Lower-control limit as 1.216 and the Upper-control-limit as 1.414. So I estimated that the mean consumption of soft drink per person (50 000 people in total) is between 1.216 and 1.414.
This means that the total average sales of soft drinks (not just Pepsi) per week is between 60800 [50000 students * 1.216] and 70700 [50000 * 1.414]. So Pepsi's market share ranges from 36.2% [22000/50000] and 31.1% [22000/70700]
The problem I have is I don't know how to "use this estimate to compute estimates of the annual profits". I mean, I thought that was already done when Pepsi's profits given their current sales level was computed. I seriously don't know what they're looking for. Or I'm I estimating the wrong population parameter? Maybe I need to conduct an hypothesis test?
This question continues on to say that "A recent graduate of a business program believes that a survey of the university's students can apply the needed information. Accordingly, she organizes a survey that asks 500 students to keep track of the number of soft drinks they purchase on campus over the next 7 days. Perform the statistical analysis to extract the needed information from the data. Estimate with 95% confidence the parameter that is at the core of the decision problem. Use the estimate to compute estimates of the annual profit. Assume that Coke and Pepsi drinkers would be willing to buy either product in the absence of the first choice.
a. On the basis of maximizing profits from sales of soft drinks at the university, should Pepsi agree to the exclusivity agreement?
b. Write a report to the company's executives describing your analysis?"
The sample size is 500. I calculated it's mean to be exactly 1.316 and the standard deviation to be 1.114733. Because the population standard deviation in the question is not given, I used the confidence Interval Estimator of the population mean when the stadard deviation is unknown to find a range in which the population mean falls (to make an inference about the mean). The formula I used is xbar ± tα/2(s/√n).
Using the t-table (the t-value I used is 1.960), I calculated the Lower-control limit as 1.216 and the Upper-control-limit as 1.414. So I estimated that the mean consumption of soft drink per person (50 000 people in total) is between 1.216 and 1.414.
This means that the total average sales of soft drinks (not just Pepsi) per week is between 60800 [50000 students * 1.216] and 70700 [50000 * 1.414]. So Pepsi's market share ranges from 36.2% [22000/50000] and 31.1% [22000/70700]
The problem I have is I don't know how to "use this estimate to compute estimates of the annual profits". I mean, I thought that was already done when Pepsi's profits given their current sales level was computed. I seriously don't know what they're looking for. Or I'm I estimating the wrong population parameter? Maybe I need to conduct an hypothesis test?