Question

# In a Pew Research Center poll of Internet users aged 18-29, 53% said that they use Instagram. We want to use a 0.05 significance level to test the claim that the majority of Internet users aged 18-29 use Instagram. What should we conclude about the original claim?

Solution

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Given:

$\hat{p}=53\%=0.53$

$n=532$

$P=0.0827$

$\alpha=0.05$

Given claim: Majority or more than 50%

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is equal to the value mentioned in the claim. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.

$H_0:p=50\%=0.50$

$H_a:p>0.50$

Determine the value of the test-statistic:

$z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0(1-p_0)}{n}}}=\dfrac{0.53-0.50}{\sqrt{\dfrac{0.50(1-0.50)}{532}}}\approx 1.38$

If the P-value is smaller than the significance level $\alpha$, then reject the null hypothesis:

$P=0.0827>0.05\Rightarrow \text{ Fail to reject } H_0$

There is not sufficient evidence to support the claim that the majority of Internet users ages 18-29 use Instagram.

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