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

Tazmin Horton 2020-12-02 Answered
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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Expert Answer

Theodore Schwartz
Answered 2020-12-03 Author has 99 answers

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:
H0:p<=0.60.
That is, the proportion of Americans are able to correctly interpret is not more than 0.60.
Alternative hypothesis:
Ha: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
p^=X/n
=2065/3278
=0.6300
then,the test statistic is
z=(p^p)((p(1p))/n)
=(0.63000.60)((0.60(10.60))/3278)
=(3278(0.03))(0.24)
=3.51
Step 4
The p value is obtained by using EXCEL
P-value=p(Z>3.51)
=1p(z<3.51)
=10.999776   [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.

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