Answer:
We conclude that the proportion of Americans who prefer to drink DD coffee is actually more than what was advertised.
Step-by-step explanation:
We are given that in a recent Dunkin Donuts (DD) commercial, it states that 58% of Americans prefer to drink their coffee.
Of the five hundred randomly selected people who were asked if they preferred DD coffees, 325 said they did.
<em>Let p = proportion of Americans who prefer to drink DD coffee</em>
SO, <u>Null Hypothesis</u>, : p
58% {means that the proportion of Americans who prefer to drink DD coffee is actually less than or equal to what was advertised}
<u>Alternate Hypothesis</u>, : p > 58% {means that the proportion of Americans who prefer to drink DD coffee is actually more than what was advertised}
The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of people who prefer to drink DD coffee in a sample of 500 people =
= 65% or 0.65
n = sample of people = 500
So, <em><u>test statistics</u></em> =
= 3.282
<em>Now at 0.05 significance level, the z table gives critical value of 1.6449 for right-tailed test. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.</em>
Therefore, we conclude that the proportion of Americans who prefer to drink DD coffee is actually more than what was advertised.