Question

A Rochester newspaper claim states that more than 60% of Rochester residents root for the Buffalo Bills football team. A recent survey random survey of 387 Rochester residents showed 254 of them root for the Bills. Is there enough evidence at the 0.05 level of significance to prove the claim made by the newspaper is correct? What is the probability of a Type I Error here?
a. Write the null and alternative hypotheses in Word b. List any necessary requirements in Word .e. What can you conclude about your hypothesis (in words) based on these results?

Answer 1

a) As we are testing here whether more than 60% of Rochester residents root for the Buffalo Bills football team, therefore the null and the alternate hypothesis here are given as:

b) The requirements here is that the population size is large enough which is a valid assumption here. Also that the sample drawn is from the population representative sample.

The sample proportion here is computed as:

p = x/n = 254 / 387 = 0.6563

The test statistic here is computed as:

Now as this is a one tailed test, the p-value here is computed from the standard normal tables as:

p = P(Z > 2.2608) = 0.0119

As the p-value here is 0.0119 < 0.05 which is the level of significance, therefore the test is significant and we can reject the null hypothesis and conclude that we have sufficient evidence that more than 60% of Rochester residents root for the Buffalo Bills football team,