The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 88.9 seconds. A manager devises a new drive-through system that he believes will decrease wait time. As a test, he initiates the new system at his restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts (a) and (b) below. 103.3 79.2 69.5 95.7 58.6 87.7 73.8 72.7 64.2 85.3 Click the icon to view the table of correlation coefficient critical values (a) Because the sample size is small, the manager must verify that the wait time is normally distributed and the sample does not contain any outliers. The normal probability plot is shown below and the sample correlation coefficient is known to be r 0.992. Are the conditions for testing the hypothesis satisfied? Expected z-score 2- Yes,the conditions satisfied. The normal probability plot linear enough, since the correlation coefficient is greater than the critical value. is are 1- 0- 60 5 90 105 -1- -2 Time (sec) (b) Is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of a 0.01 i Critical values First determine the appropriate hypotheses. 88.9 Но Sample Size, n Sample Size, n Critical Value Critical Value 88.9 H1: 5 0.880 16 0.941 0.888 17 0.944 Find the test statistic. 0.946 0.898 7 18 0.906 19 0.949 to 9 0.912 20 0.951 0.918 (Round to two decimal places as needed.) 10 21 0.952 0.954 11 0.923 22 Find the P-value 12 0.928 23 0.956 13 0.932 24 0.957 0.935 0.959 14 25 Click to select your answer(s). 0.939 0.960 15 30 Find the P-value The P-value is (Round to three decimal places as needed.) Use the a 0.01 level of significance. What can be concluded from the hypothesis tesť? A. The P-value is less than the level of significance so there is sufficient evidence to conclude the new system is effective B. The P-value is less than the level of significance so there is not sufficient evidence to conclude the new system is effective. C. The P-value is greater than the level of significance so there is sufficient evidence to conclude the new system is effective. D. The P-value is greater than the level of significance so there is not sufficient evidence to conclude the new system is effective

The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 88.9 seconds. A manager devises a new drive-through system that he believes will decrease wait time. As a test, he initiates the new system at his restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts (a) and (b) below. 103.3 79.2 69.5 95.7 58.6 87.7 73.8 72.7 64.2 85.3 Click the icon to view the table of correlation coefficient critical values (a) Because the sample size is small, the manager must verify that the wait time is normally distributed and the sample does not contain any outliers. The normal probability plot is shown below and the sample correlation coefficient is known to be r 0.992. Are the conditions for testing the hypothesis satisfied? Expected z-score 2- Yes,the conditions satisfied. The normal probability plot linear enough, since the correlation coefficient is greater than the critical value. is are 1- 0- 60 5 90 105 -1- -2 Time (sec) (b) Is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of a 0.01 i Critical values First determine the appropriate hypotheses. 88.9 Но Sample Size, n Sample Size, n Critical Value Critical Value 88.9 H1: 5 0.880 16 0.941 0.888 17 0.944 Find the test statistic. 0.946 0.898 7 18 0.906 19 0.949 to 9 0.912 20 0.951 0.918 (Round to two decimal places as needed.) 10 21 0.952 0.954 11 0.923 22 Find the P-value 12 0.928 23 0.956 13 0.932 24 0.957 0.935 0.959 14 25 Click to select your answer(s). 0.939 0.960 15 30 Find the P-value The P-value is (Round to three decimal places as needed.) Use the a 0.01 level of significance. What can be concluded from the hypothesis tesť? A. The P-value is less than the level of significance so there is sufficient evidence to conclude the new system is effective B. The P-value is less than the level of significance so there is not sufficient evidence to conclude the new system is effective. C. The P-value is greater than the level of significance so there is sufficient evidence to conclude the new system is effective. D. The P-value is greater than the level of significance so there is not sufficient evidence to conclude the new system is effective

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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