This case study is about a study on coffee consumption of people that live in th
ID: 3324632 • Letter: T
Question
This case study is about a study on coffee consumption of people that live in the United States. In total, 92 neople were randomly selected and data was gathered regarding the annual consumption of coffee in gallons. Of these 92, 51 were females and 41 were males. ProPor on 1. A consumer group claims that morethane 2% of people choose coffee rather than other beverages as their preferred drink in the moming. In the sample of 92 people, 68 reported that they prefer coffee. At -0.03, is there enough evidence to support the consumer group's claim? (12 points)Explanation / Answer
Solution:-
1)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.62
Alternative hypothesis: P > 0.62
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.03. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.05061
z = (p - P) /
z = 2.35
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 2.35. Thus, the P-value = 0.0094
Interpret results. Since the P-value (0.0094) is less than the significance level (0.03), we cannot accept the null hypothesis.
We can conclude that we have sufficient evidence that proportion is more than 0.62.