Question

Becky Sharp is trying to create an estimate for the amount of time a carriage ride from Brighton to the city of London takes. She asks her friends and acquaintances to record the time spent traveling if they make the trip during the month of June. Out of the 85 trips, She finds a mean travel time of 660 minutes, with a standard deviation of 80 minutes.

a)Are there any issues with creating a confidence interval if our population is all carriage rides from Brighton to London? Explain briefly.

b)Regardless of your answer for part a, create a 98% confidence interval for the population mean duration of the journey

Answer 1

a)Are there any issues with creating a confidence interval if our population is all carriage rides from Brighton to London?

All the assumptions are satisfied:

1. large sample size

but there is no information of population

b)

The provided sample mean is 660 and the sample standard deviation is 80. The size of the sample is n = 85 and the required confidence level is 98%.

The number of degrees of freedom are df = 85 - 1 = 84 , and the significance level is α=0.02.

Based on the provided information, the critical t-value for α=0.02 and df = 84 degrees of freedom is t_c = 2.372

The 98% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 98 % confidence for the population mean μ is