Based on data obtained from A.C. Nielsen, the mean # of televisions in a household in the United States is 2.24. Assume the population standard deviation number of television sets in the United States is 1.38 a.) Describe the sampling distribution for all sample sizes of n = 40. b.) A random sample of 40 households results in a sample mean of 2.55 tv sets per household. What is the probability of obtaining a sample mean of at least 2.55 if the population mean is 2.24? Does this contradict the results reported by A.C. Nielsen? c.) Construct a 95% confidence interval for the sample mean. How does this support your conclusion on part b? d.) Which would be more likely to happen…one household to have 3 televisions or a sample of 40 households to have a mean of 3 televisions? Explain.
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.
Based on data obtained from A.C. Nielsen, the
a.) Describe the sampling distribution for all sample sizes of n = 40.
b.) A random sample of 40 households results in a sample mean of 2.55 tv sets per household. What is the probability of obtaining a sample mean of at least 2.55 if the population mean is 2.24? Does this contradict the results reported by A.C. Nielsen?
c.) Construct a 95% confidence interval for the sample mean. How does this support your conclusion on part b?
d.) Which would be more likely to happen…one household to have 3 televisions or a sample of 40 households to have a mean of 3 televisions? Explain.
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