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<h1>Rcode for inference with one sample proportions</h1>
<p>Simulate 100 coin tosses</p>
<pre><code class="r">heads <- rbinom(1, size = 100, prob = 0.5)
</code></pre>
<p>Test whether about 50% heads came up in these coin tosses. This uses the normal approximation
to the binomial distribution with or without the continuity correction</p>
<pre><code class="r">prop.test(heads, 100) # continuity correction TRUE by default
</code></pre>
<pre><code>##
## 1-sample proportions test with continuity correction
##
## data: heads out of 100, null probability 0.5
## X-squared = 0.25, df = 1, p-value = 0.6171
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
## 0.4280 0.6296
## sample estimates:
## p
## 0.53
</code></pre>
<pre><code class="r">prop.test(heads, 100, correct = FALSE) # without continuity correction
</code></pre>
<pre><code>##
## 1-sample proportions test without continuity correction
##
## data: heads out of 100, null probability 0.5
## X-squared = 0.36, df = 1, p-value = 0.5485
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
## 0.4329 0.6249
## sample estimates:
## p
## 0.53
</code></pre>
<pre><code class="r">prop.test(heads, 100, conf.level = 0.95) # confidence level of 0.95 is the default
</code></pre>
<pre><code>##
## 1-sample proportions test with continuity correction
##
## data: heads out of 100, null probability 0.5
## X-squared = 0.25, df = 1, p-value = 0.6171
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
## 0.4280 0.6296
## sample estimates:
## p
## 0.53
</code></pre>
<p>The exact test is based on binomial probabilities:</p>
<pre><code class="r">binom.test(heads, 100)
</code></pre>
<pre><code>##
## Exact binomial test
##
## data: heads and 100
## number of successes = 53, number of trials = 100, p-value = 0.6173
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
## 0.4276 0.6306
## sample estimates:
## probability of success
## 0.53
</code></pre>
<p>Save the output in an object named temp.</p>
<pre><code class="r">temp <- prop.test(heads, 100)
</code></pre>
<p><code>names(temp)</code> shows us what output is generated and the names of the output objects.</p>
<p>Confidence interval for the proportion of heads</p>
<pre><code class="r">temp$conf.int
</code></pre>
<pre><code>## [1] 0.4280 0.6296
## attr(,"conf.level")
## [1] 0.95
</code></pre>
<p>Estimated proportion</p>
<pre><code class="r">temp$estimate
</code></pre>
<pre><code>## p
## 0.53
</code></pre>
<p>Pvalue for the hypothesis test \( H_0: p=0.5 \) versus \( H_1: p \ne 0.5 \)</p>
<pre><code class="r">temp$p.value
</code></pre>
<pre><code>## [1] 0.6171
</code></pre>
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