The mayor is interested in finding a 95% confidence interval for the mean number of pounds of trash per person per week that is generated in city. The study included 219 residents whose mean number of pounds of trash generated per person per week was 35.7 pounds and the standard deviation was 6.5 pounds.
1.a. To compute the confidence interval use a ? z t distribution.
b. With 95% confidence the population mean number of pounds per person per week is between and pounds.
c. If many groups of 219 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about percent will not contain the true population mean number of pounds of trash generated per person per week.
2.A fitness center is interested in finding a 95% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 240 members were looked at and their mean number of visits per week was 2.3 and the standard deviation was 2.7.
a. To compute the confidence interval use a ? t z distribution.
b. With 95% confidence the population mean number of visits per week is between and visits.
c. If many groups of 240 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week.
3.You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=77.4σ=77.4. You would like to be 95% confident that your estimate is within 5 of the true population mean.How large of a sample size is required?
[Do not round mid-calculation. However,use a critical value rounded to three decimal places — this is important for the system to check answers correctly.]