Question

Use the survey results given in Exercise 1 and use a 0.05 significance level to test the claim that the majority of adults learn about medical symptoms more often from the internet than from their doctor.

Short answer

There is enough evidence at 0.05 level of significance to support the claim that the majority of adults learn about medical symptoms more often from the internet than from their doctor.

Step-by-step solution

Given information

The sample number of adults is\(n = 2015\).

Number of adults who said that they learn about medical symptoms more often from the internet than from their doctor is 1108 adults who. The level of confidence is 95%.

State the null and alternate hypotheses

Let p be the true representative of the population proportionof adults who learn about medical symptoms more often from the internet than from their doctor.

The researcher claimsthat the majority of adults learn about medical symptoms more often from the internet than from their doctor.So, the statistical hypotheses are formed as shown:

\(\begin{aligned}{l}{H_0}:p = 0.50\\{H_1}:p > 0.50\end{aligned}\)

Calculate the level of significance and critical value

As the level of confidence is 95%, the level of significance is 0.05.

From the Z-table, the right-tailed critical value at 0.05 level of significance is 1.645.

Calculate the sample proportion

The sample proportion of adults who said that they learn about medical symptoms more often from the internet than from their doctor is

\(\begin{aligned}{c}\hat p = \frac{{1108}}{{2015}}\\ = 0.549876.\end{aligned}\)

Therefore, the sample proportion is \(0.549876\).

Calculate the test statistic

The test statistic is computed below:

\(\begin{aligned}{c}Z = \frac{{\hat p - p}}{{\sqrt {\frac{{p\left( {1 - p} \right)}}{n}} }}\\ = \frac{{0.549876 - 0.50}}{{\sqrt {\frac{{0.50\left( {1 - 0.50} \right)}}{{2015}}} }}\\ = 4.4777\end{aligned}\)

Thus, the value of the test statistic is 4.48.

State the decision

Since the calculated value (4.4889) of the test statistic is greater than the critical value (1.645), the null hypothesis is rejected.

Provide the conclusion

There is enough evidence at 0.05 level of significance to support the claim that the majority of adults learn about medical symptoms more often from the internet than from their doctor.