Cox Communications, the primary cable provider in Omaha, NE, claims to have excellent customer service. In fact, the company advertises that a technician will arrive approximately 30 minutes after a service call is placed. One frustrated customer believes this is not accurate, claiming it takes longer than 30 minutes for a technician to arrive. The customer puts a survey on the Nextdoor app asking other Cox customers what their experience has been. Only 9 people responded, with a mean of 32.9 minutes and standard deviation of 3.4 minutes. Test the customer's claim with a 0.025 level of significance. For the same problem as part A, construct an appropriate confidence interval based on the alpha level in A to support your conclusion from part A. Recall, if you rejected the null in part A, then your expected mean should not be included in the interval. If you failed to reject the null hypothesis, then the hypothesized mean should be in the interval. You should only need the appropriate critical value and margin of error in addition to values from part A. Correctly round your results to one decimal place in your conclusion sentence and be sure to state that it supports your decision to reject or fail to reject based on whether the hypothesized value falls in the interval.
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.
- Cox Communications, the primary cable provider in Omaha, NE, claims to have excellent customer service. In fact, the company advertises that a technician will arrive approximately 30 minutes after a service call is placed. One frustrated customer believes this is not accurate, claiming it takes longer than 30 minutes for a technician to arrive. The customer puts a survey on the Nextdoor app asking other Cox customers what their experience has been. Only 9 people responded, with a mean of 32.9 minutes and standard deviation of 3.4 minutes. Test the customer's claim with a 0.025 level of significance.
- For the same problem as part A, construct an appropriate confidence interval based on the alpha level in A to support your conclusion from part A. Recall, if you rejected the null in part A, then your expected mean should not be included in the interval. If you failed to reject the null hypothesis, then the hypothesized mean should be in the interval. You should only need the appropriate critical value and margin of error in addition to values from part A. Correctly round your results to one decimal place in your conclusion sentence and be sure to state that it supports your decision to reject or fail to reject based on whether the hypothesized value falls in the interval.
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