Question

A survey of n = 50 people reveals that the proportion of residents in a community who take the bus to work is 0.15. Is this significantly different from the statewide average of 0.10? Use a significance level of 0.05. Write down the null and alternative hypotheses, find the test statistic and the p-value, and state your conclusion.

Answer 1

To test against

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of test statistic =

and P-value =

Since P-value > 0.05, so we fail to reject H₀ at 5% level of significance and we can conclude that the proportion of residents in a community who take the bus to work is not significantly different from the statewide average of 0.10.