Math 136 Introduction to Statistics Name:
Quiz 6A Proportions ID Num:
Sampling Parameters Some Formulas may be useful:
µx¯ = µ µpˆ = p
σx¯ =
σ√
n
σpˆ =

p(1− p)
n
Sketch and shade relevant parts to find probabilities for FULL CREDIT.
1. (6 points) An estimate in 2020 found that roughly 20% of Americans were hesitant about the
COVID-19 vaccines.
Suppose we take a sample of 90 individuals.
(a) Describe the sampling distribution of the proportion of Americans who are hesitant about
the COVID-19 vaccines.
(b) Sketch and shade the relevant region to find the probability that the sample proportion will
be more than 0.28.
(c) What could you say if you take a sample and obtain a sample proportion larger than 0.28?
Please go on to the next page. . .
2. (8 points) A Gallup poll found that 493 of 1050 adult Americans believe it is the responsibility of
the federal government to make sure that all Americans have healthcare coverage.
(a) Based on the results of this survey, obtain a point estimate for the proportion of adult
Americans who believe it is the responsibility of the federal government to make sure all
Americans have healthcare coverage.
(b) Suppose we want to use our sample data to obtain a confidence interval. What conditions do
you check are satisfied before proceeding? Does our sample data show that we can obtain a
confidence interval?
(c) Answer the following parts when constructing a 90% confidence interval for the proportion of
adult Americans who believe it is the responsibility of the federal government to make sure
all Americans have helathcare coverage.
Statcrunch Command Used:
Interval:
Interpretation:
(d) During the last voting cycle, it was found that 43% of adult Americans believed it is the
responsibility of the federal government to make sure that all Americans have healthcare
coverage. Is there evidence to say that the percentage has changed now? Explain.
End of Quiz