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 86.9 seconds. A manager devises a new drive-through system that she believes will decrease wait time. As a test, she initiates the new system at her 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. 105.4 81.0 68.5 94.4 59.8 85.5 73.1 69.4 65.0 87.9 Click the icon to view the table of correlation coefficient critical values. t_0 = (Round to two decimal places as needed.) Find the P-value. The P-value is (Round to three decimal places as needed.) Use the alpha = 0.05 level of significance. What can be concluded from the hypothesis test? 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 greater than the level of significance so there is sufficient evidence to conclude the new system is effective. C. The P-value is greater than the level of significance so there is not sufficient evidence to conclude the new system is effective. D. The P-value is less than the level of significance so there is not sufficient evidence to conclude the new system is effective.
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H0: The new system does not decrease the wait time (mean wait time is equal to or greater than 86.9 seconds). H1: The new system decreases the wait time (mean wait time is less than 86.9 seconds). Now, let's calculate the mean and standard deviation of the Show more…
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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 87 seconds. A manager devises a new drive-through system that she believes will decrease wait time. To test this, she initiates the new system at her 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. (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 = 0.977. Are the conditions for testing the hypothesis satisfied? Yes, the conditions are satisfied. The normal probability plot is linear enough, since the correlation coefficient is greater than the critical value. (b) Is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of α = 0.01. First determine the appropriate hypotheses. Find the test statistic. Find the P-value. Use the α = 0.01 level of significance. What can be concluded from the hypotheses? The P-value is greater than the level of significance, so there is not sufficient evidence to conclude that the new system is effective.
Sri K.
The mean waiting time at the drive-through of a fast-food restaurant form the time an order is placed to the time the order is received is 84.3 seconds. A manager devises a new drive-through system that he believes will decrease the wait time. To test his claim, he initiates the new system at his restaurant and measures the wait time for 45 randomly selected orders and finds the sample mean to be 81.9 and a sample standard deviation of 17.3. Using a significance level of 0.01, has the wait time significantly decreased? Select the appropriate hypothesis statements for this test. what is the t stat and p-value
Madhur L.
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 87.9 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. 102.7 67.0 56.8 76.4 67.6 82.1 93.8 85.6 72.6 85.4 Critical values Sample Size, n Critical Value Sample Size, n Critical Value 5 0.880 16 0.941 6 0.888 17 0.944 7 0.898 18 0.946 8 0.906 19 0.949 9 0.912 20 0.951 10 0.918 21 0.952 11 0.923 22 0.954 12 0.928 23 0.956 13 0.932 24 0.957 14 0.935 25 0.959 15 0.939 30 0.960 (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=0.993. Are the conditions for testing the hypothesis satisfied? ▼ Yes, No, the conditions ▼ are not are satisfied. The normal probability plot ▼ is not is linear enough, since the correlation coefficient is ▼ greater less than the critical value. (b) Is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of alpha equals 0.01α=0.01. First determine the appropriate hypotheses. H0: ▼ p σ μ ▼ = < > ≠ 87.9 H1: ▼ σ p μ ▼ > < = ≠ 87.9 Find the test statistic. t0=__?__ Find the P-value. The P-value is __?__ . (Round to three decimal places as needed.) Use the α=0.01 level of significance. What can be concluded from the hypothesis test? A. The P-value is less than the level of significance so there is not sufficient evidence to conclude the new system is effective. B. The P-value is greater than the level of significance so there is sufficient evidence to conclude the new system is effective. C. The P-value is greater than the level of significance so there is not sufficient evidence to conclude the new system is effective. D. The P-value is less than the level of significance so there is sufficient evidence to conclude the new system is effective.
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