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.

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.