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?

Question
Scatterplots
asked 2020-12-02
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?

Answers (1)

2020-12-03
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:
\(H_0: p<=0.60\)</span>.
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
\(hatp= X/n\)
\(=2065/3278\)
=0.6300
then,the test statistic is
\(z=(hatp-p)/sqrt ((p(1-p))/n)\)
\(=(0.6300-0.60)/sqrt ((0.60(1-0.60))/3278)\)
\(=(sqrt3278(0.03))/sqrt(0.24)\)
=3.51
Step 4
The p value is obtained by using EXCEL
P-alue=p(Z>3.51)
=1-p(z
=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.
0

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