Question

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 the city. The study included 174 residents whose mean number of pounds of trash generated per person per week was 37.4 pounds and the standard deviation was 8.9 pounds. Round answers to 3 decimal places where possible.

Fill in the blanks

1.With 95% confidence the population mean number of pounds per person per week is between ______ and _______ pounds.

2. If many groups of 174 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.

Answer 1

1.

The provided sample mean is 37.4 and the sample standard deviation is s = 8.9 . The size of the sample is n = 174 and the required confidence level is 95%.

The number of degrees of freedom are df = 174 - 1 = 173 , and the significance level is α=0.05.

Based on the provided information, the critical t-value for α=0.05 and df = 173 degrees of freedom is t_c = 1.974

The 95% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 95 % confidence for the population mean μ is

CI = (37.4 - 1.332, 37.4 + 1.332)

CI = (36.068, 38.732)

which completes the calculation.

1.With 95% confidence the population mean number of pounds per person per week is between 36.068 and 38.732 pounds.

2. If many groups of 174 randomly selected members are studied, then a different confidence interval would be produced from each group. About 95 percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about 5 percent will not contain the true population mean number of pounds of trash generated per person per week.