14. Bank Lines The Jefferson Valley Bank once had a separate customer waiting li

Question

14. Bank Lines The Jefferson Valley Bank once had a separate customer waiting line at each teller window, but it now has a single waiting line that feeds the teller windows as vacancies occur. The standard deviation of customer waiting times with the old multiple-line configura tion was 1.8 min. Listed below is a simple random sample of waiting times (minutes) with thoe single waiting line. Use a 0.05 significance level to test the claim that with a single waiting line, the waiting times have a standard deviation less than 1.8 min. What improvement occurred when banks changed from multiple waiting lines to a single waiting line!? 6.5 6.6 6.7 6.8 7.17.3 7.4 7.7 7.7 7.7 a. Check requirements first. b. If requirements are met, list each of the 8 steps to test the hypothesis stated in the problem. Remember at Step 5 to write down the StatCrunch method you use

Explanation / Answer

Test and CI for One Variance: C4

Method

Null hypothesis         = 1.8
Alternative hypothesis < 1.8

The chi-square method is only for the normal distribution.
The Bonett method is for any continuous distribution.

Statistics

Variable   N StDev Variance
C4        10 0.477     0.227

95% One-Sided Confidence Intervals

                      Upper Bound   Upper Bound
Variable Method        for StDev for Variance
C4        Chi-Square        0.784         0.615
          Bonett            0.695         0.482

Tests

                           Test
Variable Method      Statistic DF P-Value
C4        Chi-Square       0.63   9    0.000
          Bonett              —   —    0.000

p-value = 0.000 < 0.05

hence we reject the null

there is significant evidence that sd is less than 1.8

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