Question

In: Statistics and Probability

please assume all samples are simple random samples, and all populations are normally distributed. for any...

please assume all samples are simple random samples, and all populations are normally distributed. for any calculator quantity that is to be used in a further calculation involving multiplication division powers or Roots at least four significant figures should be used unless exact

at McDonalds a sample of 81 drive-thru customers revealed that there drive through wait time had a mean of 4.87 minutes with standard deviation of .52 minutes

a. construct a 95% confidence interval estimate (2 DP) of the mean customer drive-thru wait time for the McDonald's and interpret the results in simple terms

b. Can the manager of McDonalds be 95% confident based upon the sample of customers, that the mean customer drive-thru wait time is less than 5.4 minutes?

Solutions

Expert Solution

a)

95% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 81- 1 ) = 1.99
4.87 ± 1.99 * 0.52/√(81)
Lower Limit = 4.87 - 1.99 * 0.52/√(81)
Lower Limit = 4.76
Upper Limit = 4.87 + 1.99 * 0.52/√(81)
Upper Limit = 4.98
95% Confidence interval is ( 4.76 , 4.98 )

Interpretation = We are 95% confident that the mean customer drive-thru wait time for the McDonald's

is between 4.76 min and 4.98 min.

b)

Since 5.4 is not contained in confidence interval and all values in confidence interval are less than 5.4,

We have sufficient evidence to conclude that mean customer drive-thru wait time is less than 5.4 minutes.

orchestra answered 2 years ago
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