Simone Lahey is a district vice president of a bank. She is receiving complaints from bank customers about the amount of time customers have to wait in the Mineola branch. She is investigating whether the population mean wait time of the Mineola branch is greater than the population mean wait time of the Westbury branch. Simone carefully reviews studies of the mean wait times conducted in the past and assumes that the population standard deviation is 1.09 minutes in the Mineola branch and 0.96 minute in the Westbury branch. Simone conducts a survey at each branch over a period of time by randomly selecting customers who wait in line and then recording the customers' wait times in minutes. The results of the survey are displayed in the table shown below. Let α=0.10, μ1 be the population mean wait time for customers in the Mineola branch, and μ2 be the population mean wait time for customers in the Westbury branch. If the test statistic is z≈1.84 and the rejection region is greater than z0.10≈1.282, what conclusion could be made about the population mean wait time for customers in the two branches? Identify all of the appropriate conclusions. Mineola Westbury x¯¯¯1=3.06 minutes x¯¯¯2=2.87 minutes n1=194 n2=205 Select all that apply: A. Fail to reject the null hypothesis. B. Reject the null hypothesis. C. There is sufficient evidence at the α=0.10 level of significance to conclude that the population mean wait time for customers in the Mineola branch is greater than the population mean wait time for customers in the Westbury branch. D. There is insufficient evidence at the α=0.10 level of significance to conclude that the population mean wait time for customers in the Mineola branch is greater than the population mean wait time for customers in the Westbury branch.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Simone Lahey is a district vice president of a bank. She is receiving complaints from bank customers about the amount of time customers have to wait in the Mineola branch. She is investigating whether the population
| Mineola | Westbury |
|---|---|
| x¯¯¯1=3.06 minutes | x¯¯¯2=2.87 minutes |
| n1=194 | n2=205 |
Select all that apply:
A. Fail to reject the null hypothesis.
B. Reject the null hypothesis.
C. There is sufficient evidence at the α=0.10 level of significance to conclude that the population mean wait time for customers in the Mineola branch is greater than the population mean wait time for customers in the Westbury branch.
D. There is insufficient evidence at the α=0.10 level of significance to conclude that the population mean wait time for customers in the Mineola branch is greater than the population mean wait time for customers in the Westbury branch.
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