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Question

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Don Sumner · Accepted Answer

We are given that 79% of all job seekers used social media in their job search in 2018. We want to test whether the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds this proportion. We are given a sample of 370 22- to 30-year-old job seekers, of which 310 use social media in their job search.
Our null hypothesis is that the proportion of 22- to 30-year-old job seekers who use social media in their job search is equal to or less than 79%. Our alternative hypothesis is that the proportion of 22- to 30-year-old job seekers who use social media in their job search is greater than 79%. We can set the significance level,

α

, to 0.05.
Using the sample data, we can calculate the sample proportion of 22- to 30-year-old job seekers who use social media in their job search:

\hat{p} = \frac{310}{370} = 0.8378

We can also calculate the standard error of the sample proportion:

S E = \sqrt{\frac{p (1 - p)}{n}}

where

p

is the population proportion and

n

is the sample size. Since we do not know the population proportion, we will use the sample proportion as an estimate:

S E = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}} = \sqrt{\frac{0.8378 (1 - 0.8378)}{370}} = 0.0231

We can now calculate the test statistic:

z = \frac{\hat{p} - p_{0}}{S E}

where

p_{0}

is the hypothesized population proportion under the null hypothesis. Using

p_{0} = 0.79

, we get:

z = \frac{0.8378 - 0.79}{0.0231} = 2.071

We can find the p-value by looking up the area to the right of the test statistic in a standard normal distribution table. The p-value is the probability of getting a test statistic as extreme as ours, assuming the null hypothesis is true. Since this is a one-tailed test (our alternative hypothesis is one-sided), we only need to look at the area to the right of the test statistic.
The area to the right of

z = 2.071

is 0.0198. Therefore, the p-value is 0.0198.
Since the p-value is less than

α = 0.05

, we reject the null hypothesis. We can conclude that there is evidence to suggest that the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of all job seekers who use social media in their job search.

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