Question

1. In 2012 16% of Americans were enrolled in Medicare. It has been hypothesized that Florida has a higher percentage of people enrolled in Medicare since a lot of the residents are retirees who moved south to warmer climates. In a random sample of 150 residents of Florida, 29 of the 150 (19%) said they were enrolled in Medicare. f. Using the plot created in part e, calculate the estimated p-value used to answer the research question of interest. Make sure to clearly show how you obtained this value. (2 points) g. Using the estimated p-value found in part f, give the conclusion for this study in context of the research question. (3 points)

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P < 0.16
Alternative hypothesis: P > 0.16

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. 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 (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.02993
z = (p - P) / S.D

z = 1.114

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 1.114.

Thus, the P-value = 0.133

Interpret results. Since the P-value (0.133) is greater than the significance level (0.05), we cannot accept the null hypothesis.

Do not reject H0, from the above test we do not have sufficient evidence in the favor of the claim that Florida has a higher percentage of people enrolled in Medicare since a lot of the residents are retirees who moved south to warmer climates.