The average expenditure on Valentine's Day was expected to be $108.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 48 male consumers was $138.96 , and the average expenditure in a sample survey of 35 female consumers was $61.82. Based on past surveys, the standard deviation for male consumers is assumed to be $33, and the standard deviation for female consumers is assumed to be $10. The x value is 2.576. (Round your answers to 2 decimal places.) What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females? At 99% confidence, what is the margin of error? Develop a 99% confidence interval for the difference between the two population means.
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.
The average expenditure on Valentine's Day was expected to be $108.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 48 male consumers was $138.96 , and the average expenditure in a sample survey of 35 female consumers was $61.82. Based on past surveys, the standard deviation for male consumers is assumed to be $33, and the standard deviation for female consumers is assumed to be $10. The x value is 2.576. (Round your answers to 2 decimal places.)
- What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?
- At 99% confidence, what is the margin of error?
- Develop a 99% confidence interval for the difference between the two population means.
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