Question

STD study: A 2008 CDC study estimated that 26% of young women between the ages of 14 and 19 in the U.S. were infected with at least one of the most common sexually transmitted diseases (human papillomavirus [HPV]), chlamydia, herpes simplex virus, and trichomoniasis). Is the percentage lower in your community?

Suppose that we select a random sample of 100 young women in your community. We can use a normal model for the sampling distribution because the conditions are met. We expect 26 of the 100 to be infected with at least one of the most common STDs and 74 to not be infected. So we can find the Z-score and use the applet to assess the evidence provided by the data. (The standard error is about 0.044.) Here is a link to the applet.

Suppose that in a random sample of 100 young women in your community, 20% are infected with at least one of the most common STDs

True or false? We can conclude that the percentage of all young women in your community who are infected with at least one of the most common STDs is less than 26%.

True or
False

Answer 1

Without calculating the exact p-value for the Z-score of -1.36, we cannot conclusively state whether the percentage of young women with STDs in the community is lower than the CDC's estimate of 26%. Therefore, the given statement is false as further statistical evaluation is necessary.

Step-by-step explanation:

To determine whether the percentage of young women infected with at least one of the most common STDs in your community is statistically less than the 26% estimated by the CDC, we need to consider the sample proportion and use statistical hypothesis testing. The sample proportion in this case is p = 0.20 (or 20%), which we compare to the hypothesized population proportion, p0 = 0.26. With the given standard error (SE) of about 0.044, we can calculate the Z-score, which is the number of standard errors that p is from p0.

The Z-score is calculated as follows:
Z = (p - p0) / SE
Z = (0.20 - 0.26) / 0.044
Z = -1.36

We can now look up the corresponding p-value for Z = -1.36 in a standard normal distribution table or use statistical software. If the p-value is less than the significance level (commonly 0.05), we can reject the null hypothesis and conclude that the proportion in your community is statistically significantly lower than 26%.

However, if the p-value is greater than 0.05, we do not have sufficient evidence to conclude that the proportion is lower.

Since the calculation of the exact p-value is not provided in this scenario, we cannot definitively conclude whether the percentage is statistically lower without further information.

Therefore, the statement that 'we can conclude that the percentage of all young women in your community who are infected with at least one of the most common STDs is less than 26%' is False until a p-value is calculated and compared to an alpha level.