Question

Previously, 7.1% of workers had a travel time to work of more than 60 minutes. An urban economist believes that the percentage has increased since then. She randomly selects 95 workers and finds that 10 of them have a travel time to work that is more than 60 minutes. Test the economist's belief at the a = 0.05 level of significance. What are the null and alternative hypotheses? Ho: P = 0.071 versus H 0.071 (Type integers or decimals. Do not round.) Because np. (1-P) = 6.3 < 10, the normal model may not (Round to one decimal place as needed.) used approximate P-value Find the P-value P-value = (Round to three decimal places as needed.)! Enter your answer in the answer box and then click Check Answer. Clear All part remaining

Answer 1

Since the normal model can't be applied here hence we will use the binomial model to estimate the p-value.

The p-value is equal to the probabiltiy that 10 out of 95 workers will have a travel time of more than 60 minutes.

The p-value is

$= \binom{95}{10}0.071^{10}(1-0.071)^{85} = 0.0629$

This p-value is greater than the significance level of 0.05 hence we would accept the null hypothesis and say that there is not sufficient evidence to say that the travel time for workers has increased.

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