In the current pandemic situation, customers are making greater use of grocery home delivery services. A local grocery chain wants to know how satisfied customers in Fairfax county are, on average, with their home delivery service. It surveyed 42 customers in Fairfax county and asked them to rate their satisfaction on a 100-point scale. They obtained a sample average of 82 points. This service has been provided by the grocery chain for some time and the population standard deviation of satisfaction is known to be 6.5 points. What is the population for which inferencing is being done? (narrative, no calculation) What is the population parameter for which inferencing is being done? (narrative, no calculation) At a 97% level of confidence, what is the margin of error? What is the 97% confidence interval for the population parameter? [Note: be sure to express the confidence interval in narrative form for the context of this problem.]
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.
In the current pandemic situation, customers are making greater use of grocery home delivery services. A local grocery chain wants to know how satisfied customers in Fairfax county are, on average, with their home delivery service. It surveyed 42 customers in Fairfax county and asked them to rate their satisfaction on a 100-point scale. They obtained a sample average of 82 points. This service has been provided by the grocery chain for some time and the population standard deviation of satisfaction is known to be 6.5 points.
- What is the population for which inferencing is being done? (narrative, no calculation)
- What is the population parameter for which inferencing is being done? (narrative, no calculation)
- At a 97% level of confidence, what is the margin of error?
What is the 97% confidence interval for the population parameter? [Note: be sure to express the confidence interval in narrative form for the context of this problem.]
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