In Exercises 1–3, use the following service times (in seconds) observed at lunchtime at different fast-food restaurant drive-up windows. Assume that the service times for such restaurants are
- 1. McDonald’s. Using only the service times from McDonald’s, construct a 95% confidence
interval estimate of the populationmean .
Using the service times from McDonald’s obtain a 95% confidence interval to estimate the populations mean.
Answer to Problem 1CRE
The 95% confidence interval to estimate the population mean is
Explanation of Solution
Calculation:
The data related to the service times at lunchtime for drive-up windows at McDonald’s.
t-distribution:
A random variable X is said to follow t distribution with degrees of freedom
The value of random variable X can be defined as,
Test statistic:
The test statistic is obtained as,
Level of significance:
The level of significance is
For two tail test the level of significance is,
The sample size is
Degrees of freedom:
The degrees of freedom for t distribution is
Hence, the degrees of freedom for
Critical value:
Step by step procedure to obtain the critical value from the TABLE 10.1: Critical t values, is obtained as:
- Locate the degrees of freedom of 5 from the 1st column of TABLE 10.1.
- Locate the area from the column of “0.05 area in two tails” corresponding to the degrees of freedom of 5.
The critical value is 2.571.
Mean:
Software procedure:
Step by step procedure using EXCEL to obtain Mean is given below:
- Enter the name McDonald’s in the first cell A1 of an EXCEL sheet.
- Enter the data value in that sheet corresponding to the heading McDonald’s from cell A2 to A7.
- In cell A8 enter the formula “=AVERAGE(A2:A7)”.
- Click Enter.
The output is given below:
Thus, the sample mean
Standard deviation:
Software procedure:
Step by step procedure using EXCEL to obtain Standard deviation is given below:
- Enter the name McDonald’s in the first cell A1 of an EXCEL sheet.
- Enter the data value in that sheet corresponding to the heading McDonald’s from cell A2 to A7.
- In cell A8 enter the formula “=STDEVA(A2:A7)”.
- Click Enter.
The output is given below:
Thus, the sample standard deviation
Margin of error:
The margin of error, E is defined as,
The critical value is obtained as 2.571, the sample standard deviation is
Thus, the margin of error is,
Therefore, the margin of error is approximately 69.46
Confidence interval:
The 95% confidence interval around a sample mean to estimate the true value of population mean,
Hence the confidence interval is,
Thus, the 95% confidence interval to estimate the population mean is
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