T11.11 A government report says that the average amount of money spent per U.S. household food is about $158. A random sample of 50 house- holds in a small city is selected, and their weekly spending on food is recorded. The sample data have a mean of $165 and a standard deviation of $32. Is there convincing evidence that the mean weekly spending on food in this city differs from the national figure of $1587 per week on (a) State appropriate hypotheses for performing a significance test in this setting. Be sure to define the parameter of interest. (b) The distribution of household spending in this small city is heavily skewed to the right. Explain why the Normal/Large Sample condition is met in this case. (c) The P-value of the test is 0.128. Interpret this value. What conclusion would you make?
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.
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