Question

use the given data set to complete parts (a) through (c) below (use \\( \alpha=0.05 \\) )
the linear correlation coefficient is \\( r=0.816 \\)
(round to three decimal places as needed.)
using the linear correlation coefficient found in the previous step, determine whether there
sufficient evidence to support the claim of a linear correlation between the two variables.
choose the correct answer below.
a. there is sufficient evidence to support the claim of a nonlinear correlation between th
two variables.
b. there is insufficient evidence to support the claim of a nonlinear correlation between
the two variables.
c. there is insufficient evidence to support the claim of a linear correlation between the
two variables.
d. there is sufficient evidence to support the claim of a linear correlation between the two
variables.
c. identify the feature of the data that would be missed if part (b) was completed without
constructing the scatterplot. choose the correct answer below.
a. the scatterplot reveals a perfect straight - line pattern, except for the presence of one
outlier.
b. the scatterplot reveals a perfect straight - line pattern and does not contain any outliers.
c. the scatterplot does not reveal a perfect straight - line pattern.
d. the scatterplot does not reveal a perfect straight - line pattern, and contains one outlier

Explanation:

Part (b)

Step1: Identify n and critical value

Count data points: n=11. For α=0.05, critical r≈0.602.

Step2: Compare r to critical value

Given r=0.816 > 0.602, so sufficient evidence for linear correlation.

A high linear correlation coefficient (0.816) suggests a strong linear trend, but scatterplots often reveal outliers that affect the correlation. Without a scatterplot, an outlier (if present) would be missed, even if the overall trend is nearly perfect linear.

Answer:

D. There is sufficient evidence to support the claim of a linear correlation between the two variables.

Part (c)