Question

The mean and the standard deviation of the sample of 100 bank customer waiting times are x¯

= 5.10 and s = 2.113. Calculate a t-based 95 percent confidence interval for µ, the mean of all possible bank customer waiting times using the new system. Are we 95 percent confident that µ is less than 6 minutes?. Assume normality. (Choose the nearest degree of freedom for the given sample size. Round your answers to 3 decimal places.)

  The t-based 95 percent confidence interval is [, ].

, interval is than 6.

Answer 1

Given that , n = 100 , = 5.10 and s = 2.113

We have to find a 95% confidence interval using the t distribution.

Degrees of freedom = n -1 = 99

At 95% confidence level and df = 99 , the critical value of t is t = 1.98

The confidence interval is = t * s/ n

= 5.10 0.419

= ( 4.681 , 5.519 )

The t based 95% confidence interval is (4.681 , 5.519).

Since the interval does not contain 6 within its bounds, we are 95 percent confident that µ is less than 6 minutes.