Question 1 [ 4 marks ]
As part of a lesson on statistical inference an enterprising statistics teacher gave his class of 15 students an “Ice Cream Taste Test”. The results showed that 9 students preferred the chocolate ice cream, while 6 students preferred the vanilla ice cream. Use Table 5 to determine the following confidence intervals.
- a) Estimate the true proportion of those preferring chocolate ice cream using a 90% confidence interval.
- b) Estimate the true proportion of those preferring chocolate ice cream using a 95% confidence interval.
- c) Estimate the true proportion of those preferring vanilla ice cream using a 99% confidence interval.
- d) Interpret the interval obtained in part (c) above.
Question 2 [ 5 marks ]
A survey of 100 randomly selected junior high school girls showed that 37 planned careers in a technical field. Find a 95% confidence interval for the true proportion of all junior high school girls who are planning a career in a technical field. Use the Wilson’s Score Confidence Interval. Interpret the interval.
Question 3: [ 4 marks ]
A study is planned to estimate the proportion of young adults (18-25 year olds) in Canada who smoke. How large a sample should be used to estimate the true proportion to within 0.03 with a level of confidence (reliability) 99% if
a) a pilot sample gave 0.35 as a prior estimate for p?
b) no prior estimate of p is available?
Question 4 [ 5 marks ]
When Harvey Dent flips his favourite coin 1000 times, “heads” appears 440 times. Let p be the true probability that this coin will come up “heads” when tossed.
a) Estimate p using a 95% confidence interval. Use the standard approximate confidence interval.
b) Based on the interval in part a), would you suspect that the coin is “unfair”? Explain.