Question

1. A tourist agency on the border of Canada and the United States wants to know if a majority of the proportion of visitors going to Niagara Falls are from the United States. A random survey was conducted on 150 visitors at Niagara Falls. Of those surveyed, 90 were from the United States.

a.If you were to create a confidence interval for the true proportion of visitors to Niagara Falls that are from the United States, which test statistic would you use?

b.If you found that the 95% confidence interval to estimate the true proportion of visitors to Niagara Falls that are from the United States was (0.5216, 0.6784), does this provide evidence that a majority of visitors to Niagara Falls are from the United States? Explain your answer.

c.State your null and alternative hypotheses for a hypothesis test given the above information.

d.If you found a p-value of 0.007, what would you conclude if your level of significance was 0.05? Do not forget a contextual interpretation.

Answer 1

a)

Use one-sample Z test for proportions to create confidence interval.

b)

95% confidence interval = ( 0.5216 , 0.6784 )

Since 0.50 not contained in confidence interval and all values in confidence interval are

greater than 0.50, we have sufficient evidence to support the claim that a majority of visitors to

Niagara Falls are from the United States.

c)

The null and alternative hypothesis are

H0: p = 0.50

Ha: p > 0.50

d)

Since p-value (0.007) < 0.05 significance level, Reject H0

We have sufficient evidence to conclude that a majority of visitors to Niagara Falls are from the United States.