The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 45 male consumers was $135.67, and the average expenditure in a sample survey of 37 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $32, and the standard deviation for female consumers is assumed to be $19. a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)? b. At 99% confidence, what is the margin of error (to 2 decimals)? c. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.

The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 45 male consumers was $135.67, and the average expenditure in a sample survey of 37 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $32, and the standard deviation for female consumers is assumed to be $19. a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)? b. At 99% confidence, what is the margin of error (to 2 decimals)? c. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.

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MATLAB: An Introduction with Applications

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Concept explainers

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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The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 45
male consumers was $135.67, and the average expenditure in a sample survey of 37 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be
$32, and the standard deviation for female consumers is assumed to be $19.
a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?
b. At 99% confidence, what is the margin of error (to 2 decimals)?
c. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.

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