Question

police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. listed below are shoe print lengths, foot lengths, and heights of males. construct a scatterplot, find the value of the linear correlation coefficient r, and find the p - value of r. determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. based on these results, does it appear that police can use a shoe print length to estimate the height of a male? use a significance level of α = 0.01.
shoe print (cm) | 30.4 30.4 31.1 31.5 27.2
foot length (cm) | 25.2 25.4 27.5 26.3 26.1
height (cm) | 172.6 181.5 182.3 181.7 168.6
the linear correlation coefficient is r = 0.843.
(round to three decimal places as needed.)
determine the null and alternative hypotheses.
h₀: ρ
h₁: ρ
(type integers or decimals. do not round.)

Explanation:

Step1: Identify Hypotheses Type

For testing linear correlation, the null hypothesis assumes no linear correlation (ρ = 0), and the alternative hypothesis tests for any linear correlation (ρ ≠ 0) when checking if there's a linear relationship.

Step2: Formulate Hypotheses

• Null Hypothesis ($H_0$): $

ho = 0$ (no linear correlation between shoe print length and height).

• Alternative Hypothesis ($H_1$): $

ho
eq 0$ (there is a linear correlation between shoe print length and height).

Answer:

$H_0:
ho = 0$
$H_1:
ho
eq 0$