Question

Ubisoft is a large manufacturer of video games. The Marketing Manager has hired a consultant to design a survey to determine attitudes towards the products. In addition the percentage of young adults in Quebec owning video games and the average usage rate per week are to be determined. The Marketing Manager wants to be 95% confident of the results and does not want the error to exceed 3 percentage points for video game ownership and 1 hour for average usage rate. Previous reports are not available for the percentage owning video games, but some earlier studies do indicate that the average usage rate is 15 hours with a variance of 25 hours.

a. What sample size would you recommend assuming that only the percentage of households owning video games is to be determined? Show all your calculations

b. What sample size would you recommend assuming that only the average usage rate per week is to be determined? Show all your calculations.

c. Due to budget constraints, Ubisoft decided to use a sample size of 582, and to maintain the confidence level at 95%. What is the consequence of doing so for the specified video game ownership error rate and for the average usage rate error rate? Show all your calculations.

d. The actual results of the survey showed that 30% of young adults owned video games and that the average usage rate is 13 hours (variance=16). Compute the 95% confidence interval for the usage rate per week.

e. The consultant who carried out the survey using systematic sampling found that some interviewers had skipped respondents who were hard to understand on the phone, and that some survey questions may not have been clear. She makes the following statement in her presentation to the management of the firm: “Based on the results, I can say with 95% confidence that the average young adult in Quebec who owns video games uses them for 13 hours a week. There is only a 5% probability that any mistakes that might have occurred in the survey process can affect the results”. Discuss whether the consultant is justified in making the statement she did (in quote marks).

Answer 1

(a)

(b)

The standard deviation is

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(c)

As the sample size decreases so the margin of error increases for confidence interval of percentage of households owning video games.

As the sample size increases so the margin of error decreases for confidence interval of the average usage rate per week.

(d)

Since variance is 16 so standard deviation will be

Since sample size is large so we can use z confidence interval.

(e)

No becuase respondents are skipped so we cannot take it as simple random sample. That is we cannot assume that sample truly represent the population.

And she should says that  “Based on the results, I can say with 95% confidence that the average young adult in Quebec who owns video games uses them for 13 hours a week with margin of error 0.325 hours.”.