To Test the Null Hypothesis That the Difference Between Two

question 32

Essay

To test the null hypothesis that the difference between two population proportions is equal to a nonzero constant c , use the test statistic
$z = \frac { \left( \hat { p } _ { 1 } - \hat { p } _ { 2 } \right) - c } { \sqrt { \hat { p } _ { 1 } \left( 1 - \hat { p } _ { 1 } \right) / n _ { 1 } + \hat { p } _ { 2 } \left( 1 - \hat { p } _ { 2 } \right) / n _ { 2 } } }$
As long as $n _ { 1 }$ and $n _ { 2 }$ are both large, the sampling distribution of the test statistic $z$ will be approximately the standard normal distribution. Given the sample data below, test the claim that the proportion of male voters who plan to vote Republican at the next presidential election is 15 percentage points more than the percentage of female voters who plan to vote Republican. Use the P -value method of hypothesis testing and use a significance level of 0.10 .
Men: $n _ { 1 } = 250 , x _ { 1 } = 146$
Women: $n _ { 2 } = 202 , x _ { 2 } = 103$

Understand and apply the concepts of skewness in the distribution of data.

Analyze and compare data across multiple groups or categories.

Understand the implications of removing or altering data points within a data set.

Understand the concept of variance and how to calculate it from standard deviation.

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Definitions:

Proved Reserves

Located quantities of natural resources, such as oil or gas, that can be recovered in the future with high certainty under existing economic and operational conditions.

Natural Resources

Raw materials and environmental attributes derived from nature that are used in the production of goods and services.

Proved Reserves

Proved reserves are quantities of natural resources, such as oil or natural gas, which have been discovered and are considered recoverable under current economic and operational conditions.

Petroleum

A naturally occurring liquid found beneath the Earth's surface that can be refined into fuel and other products.