Original claim: Fewer than 90 % of adults have a cell phone. The hypothesis test results in a P

step 1 We are going to use a significance level of 0 .05 and the following information. Our original cl

Original claim: Fewer than 90 % of adults have a cell phone....

Key Concepts

Alternative Hypothesis

The alternative hypothesis is the statement that contradicts the null hypothesis and represents the claim we wish to support. In this context, it is the claim that the proportion of adults with a cell phone is less than 90%, indicating a directional (one-tailed) test.

P-value

The P-value is the probability of obtaining results at least as extreme as the observed data, assuming that the null hypothesis is true. A very small P-value, such as 0.0003, suggests that the observed data is highly inconsistent with the null hypothesis, providing strong evidence in favor of the alternative hypothesis.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population parameter based on sample data. It involves setting up a null hypothesis, which represents an assumed value or status quo, and an alternative hypothesis, which is the claim we are testing against the null hypothesis.

Null Hypothesis

The null hypothesis is a statement that there is no effect or no difference, and it serves as the default or starting assumption in hypothesis testing. In a test regarding a proportion, the null hypothesis might state that the proportion of adults with a cell phone is equal to a specific value, such as 90%.

Statistical Significance

Statistical significance refers to the conclusion that the observed effect or difference is unlikely to have occurred by chance alone, according to a predetermined significance level (commonly 0.05). In this scenario, the extremely low P-value would typically lead researchers to conclude that there is statistically significant evidence to support the claim that fewer than 90% of adults have a cell phone.

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