According to the CDC, 9.1% of the population in the United States is diabetic. I

Question

According to the CDC, 9.1% of the population in the United States is diabetic. If we were to randomly select seven people from the population, what is the probability that one of those people will be diabetic?

We sample 241 people who have parents diagnosed with diabetes. Of those 241, we find that 79 have also been diagnosed. Using the relevant information provided in the previous question, determine whether there is a significant difference between the overall population and our sample of children of diabetics. Interpret the results from the calculations.

Explanation / Answer

SOlution:-

a) The probability that one of those people will be diabetic is 0.3594.

p = 9.1/100 = 0.091

n = 7, x = 1

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 1) = 0.3594

b)

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

Null hypothesis: P = 0.091

Alternative hypothesis: P 0.091

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

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 () and compute the z-score test statistic (z).

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

= 0.01853

z = (p - P) /

z = 12.78

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 two-tailed test, the P-value is the probability that the z-score is less than -12.78 or greater than 12.78.

Thus, the P-value = less than 0.0001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

Hence there is a significant difference between the overall population and our sample of children of diabetics.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.