# In 2014, the Pew Research Centers American Trends Panel sought to better understand what Americans know about science. It was observed that among a ra

In 2014, the Pew Research Centers American Trends Panel sought to better understand what Americans know about science. It was observed that among a random selection of 3278 adults, 2065 adults could correctly interpret a scatterplot. Is this good evidence that more than 60% of Americans are able to correctly interpret scatterplots?
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Theodore Schwartz

Step 1
Solution:
Let X be the number of adults correctly interpret a scatterplot and n be the sample number of adults.
From the given information, X=2065 and n=3278.
The given claim is that more than 60% of Americans are able to correctly interpret scatterplots.
State the hypotheses.
Null hypothesis:
${H}_{0}:p<=0.60$.
That is, the proportion of Americans are able to correctly interpret is not more than 0.60.
Alternative hypothesis:
${H}_{a}:p>0.60$
That is, the proportion of Americans are able to correctly interpret is more than 0.60.
Step 3:
The sample proportion is
$\stackrel{^}{p}=X/n$
$=2065/3278$
$=0.6300$
then,the test statistic is
$z=\left(\stackrel{^}{p}-p\right)\sqrt{\left(\left(p\left(1-p\right)\right)/n\right)}$
$=\left(0.6300-0.60\right)\sqrt{\left(\left(0.60\left(1-0.60\right)\right)/3278\right)}$
$=\left(\sqrt{3278\left(0.03\right)}\right)\sqrt{\left(0.24\right)}$
$=3.51$
Step 4
The p value is obtained by using EXCEL
P-value$=p\left(Z>3.51\right)$
$=1-p\left(z<3.51\right)$
$=1-0.999776$   [USING THE EXCEL FUSION]
$=0.0002$
Thus the p value is 0.0002
Step 5
Rejection rule:
If the P-value is less than or equal to 0.05, then reject the null hypothesis.
Conclusion:
Here, the P-value is 0.0002.
This is less than 0.05.
By the rejection rule, reject the null hypothesis.
Thus, there is good evidence that more than 60% of Americans are able to correctly interpret scatterplots.