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In statistical hypothesis testing, the null hypothesis (\(H_0\)) represents a general statement or default position that there is no relationship between two measured phenomena. In this exercise, it is used to test whether the proportion of adults having cell phones is indeed equal to 95%.
The null hypothesis is formulated to be tested, and if the evidence (data) is strong enough, we can reject it.
If not, we fail to reject the null hypothesis, meaning there's not enough evidence against it, and we consider it true for practical purposes.

We write the null hypothesis symbolically as: \(H_0: p = 0.95\)
The \(p\) here denotes the proportion of the entire population who have a cell phone. This hypothesis asserts that the population proportion is equal to 95%.

The alternative hypothesis (\(H_1\)) is a statement that we want to test for its validity. This hypothesis is generally represented as a situation where there is an effect, or a certain condition holds true.
In the context of our exercise, while the null hypothesis posits that the proportion of adults having cell phones is 95%, the alternative hypothesis challenges this by suggesting that fewer than 95% of adults have cell phones.
We write the alternative hypothesis as:\(H_1: p < 0.95\)

Here, the alternative hypothesis is a one-sided hypothesis because it only considers the possibility of the proportion being less than 95%, but not more than 95%.
It's important to note that the claim we are testing drives the formulation of this hypothesis. The results of statistical tests will inform whether we can reject the null hypothesis in favor of this alternative hypothesis.

A proportion refers to a part or segment of the whole, quantified as a fraction or percentage of the total. In statistical terms, it often represents the ratio of a particular occurrence to the total number of occurrences.
In the given exercise, \(p\) represents the proportion of adults who have cell phones.
We are interested in comparing this population proportion against a specific level, which is 95% in this case.
Using the sample size of 1128 adults where 87% reported having a cell phone, we can statistically test if this sample proportion (\(\frac{1128 \times 0.87}{1128}\)) supports the claim that fewer than 95% of all adults have a cell phone or not.

In hypothesis tests involving proportions, the sample proportion (\(\frac{\text{number of successes}}{\text{sample size}}\)) is compared against the claimed population proportion.