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Lesson 7 (Confidence Level and Sample Size).p.. 5. A particular brand of coffee contains an average of 112 mg of caffeine per cup with a standard deviation of 20 mg. Joshua wants to investigate the same to estimate the true population mean caffeine content correct to within 5 mg adopting 95% confidence. How many cups of the same brand of coffee does he need for a sample? 6. In a gymnasium, a physical exercise has a mean length of 30 minutes with a standard deviation of 6 minutes. A PE major wants to estimate the true mean length of the exercise with maximum error pegged at 0.5 adopting the 95% confidence interval. How many respondents does he need? 7. In a paper presentation, the average algebraic reasoning of Grade 8 students in a mathematics camp was observed to be 80 with a standard deviation of 4.2. A researcher wants to replicate the study to estimate the true population mean u to within .5 maximum error. If the 95% level of confidence is adopted, how many respondents are needed? 8. A politician engaged the services of a private opinion pollster to determine the sample size needed among his constituents to interview about their perceptions on the freedom of information bill. Previous polls revealed that approximately 62.5% are in favor of the bill: The politician adopted the 0.95 level of confidence and off the population value by at most 0.02. 9. A transportation company wants to know the amount of time it takes a bus to travel from one bus stop to the next. From past observations, the standard deviation is 5 hours. How many measurements are needed in order to be 95% certain that the maximum error of estimate will not exceed 1 hour? b. What sample size is required for a maximum error of 2 hours