MGMT2262
Tutorial Sheet #6
A researcher wanted to see if the percentage of Ipod users among those aged 18-34 has increased from 35% two years ago. A survey of 200 people in that age group showed that 84 of them own an Ipod.
1) Test the hypothesis at a 5% level of significance. (Z = 2.08; conclude the percentage has increased)
2) Suppose the level of significance had been set at 1% instead. Why would the opposite conclusion be reached? (p-value = 0.0188 > 0.01)
3) Construct a 95% confidence interval of the percentage of Ipod users in this age group. Interpret the interval. (0.3516 < p < 0.4884. The percentage of Ipod users in the 18-34 age ranges is from 35.16% to 48.84% with 95% confidence)
4) Suppose the researcher wanted to conduct a larger study. What would be the required sample size if the researcher wanted a 3% margin of error at a 95% level of confidence using the results of the first study? (1040)
5) Suppose the researcher can afford no more than 500 surveys for a follow-up study. What is the margin of error the researcher must live with? (4.33%)
Due to a tight labour market, a market research firm had difficulty retaining people in the phone room. As a result, management suspected there was more variability in the number of surveys completed per hour on one of its regular tracker studies. Historically, the number of surveys completed per hour on this study was normally distributed with an average of 3.5 and standard deviation of 0.75. For a sample of 25 hours, the standard deviation was 0.9.
6) Test the hypothesis at a 5% level of significance. (c2 = 34.56. Conclude the variability is not significantly increased)
7) In what range would the p-value fall? If the hypothesis had been tested at a 10% level of significance instead, why would the opposite conclusion be reached? (p-value is between 5% and 10%)
8) Construct a 95% confidence interval of the standard deviation. Suppose this had been set up as a two-tail test, what conclusion would be reached at a 5% level of significance? (0.7025 < s < 1.2526; we would conclude the standard deviation is not significantly changed from 0.75 since the hypothesis standard deviation of 0.75 falls in the confidence interval)