Question

Instagram Poll 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.

a. Identify the null and alternative hypotheses.

b. Using a sample size of 532, find the value of the test statistic.

c. Technology is used to find that the P-value for the test is 0.0827. What should we conclude about the null hypothesis?

d. What should we conclude about the original claim?

Short answer

a. Null Hypothesis: The proportion of internet users, aged 18-29,who use Instagram is equal to 0.5.

b. Alternative hypothesis: The proportion of internet users, aged 18-29,who use Instagram is greater than 0.5.

c. The null hypothesis fails to be rejected.

d. There is not enough evidence to support the claim that the proportion of Internet users aged 18-29 who use Instagram is more than 50%.

Step-by-step solution

Given information

In a poll, 53% of internet users aged 18-29 said they use Instagram. It is claimed that a majority of Internet users, aged 18-29, use Instagram

Hypotheses

a.

It is claimed that the majority of Internet users use Instagram.

Corresponding to the given claim, the following hypotheses are set up:

Null Hypothesis: The proportion of internet users aged 18-29 who use Instagram is equal to 0.5.

$H_0:p=0.5$

Alternative hypothesis: The proportion of internet users aged 18-29 who use Instagram is greater than 0.5.

role="math" localid="1649225974191" $H_1:p>0.5$

Important values

Here, the sample size (n) is equal to 532.

The sample proportion of Internet users aged 18-29 who use Instagram is given to be equal to:

$$\begin{gathered} \hat{p}=53\% \\ =\frac{53}{100} \\ =0.53 \end{gathered}$$

The population proportion of Internet users aged 18-29 who use Instagram is equal to 0.5.

Test statistic

b.

The value of the test statistic is computed below:

$$\begin{gathered} z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}} \\ =\frac{0.53-0.5}{\sqrt{\frac{0.5\left(1-0.5\right)}{532}}} \\ =1.384 \end{gathered}$$

Thus, z=1.384.

Decision about the null hypothesis

c.

It is given that the p-value for the test statistic value of 1.384 is equal to 0.0827.

Since the p-value is equal to 0.0827, which is greater than 0.05, the null hypothesis is rejected.

Conclusion of the test

d.

There is not enough evidence to support the claim that the proportion of Internet users aged 18-29 who use Instagram is more than 50%.