A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below. Seeds Produced 51 57 51 47.5 50 70 70 55 55 50 Sprout Percent 49.5 54.5 47 38 41 54.5 47.5 54 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? H1: ? The p-value is: (Round to four decimal places) c. Use a level of significance of a = of the study, 0.05 to state the conclusion of the hypothesis test in the context
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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Week 14: Chapter 12 - Linear Re X
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Question 3
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A biologist looked at the relationship between number of seeds a plant produces and the percent of those
seeds that sprout. The results of the survey are shown below.
Seeds Produced
51
57
51
50
70
70
55
50
Sprout Percent
49.5
54.5
47.5
47
38
41
54.5
47.5
54
a. Find the correlation coefficient: r=
Round to 2 decimal places.
b. The null and alternative hypotheses for correlation are:
Ho: ? v
H1: ?
手0
The p-value is:
(Round to four decimal places)
c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context
of the study.
O There is statistically insignificant evidence to conclude that there is a correlation between the
number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the use
of the regression line is not appropriate.
O There is statistically significant evidence to conclude that a plant that produces more seeds
will have seeds with a lower sprout rate than a plant that produces fewer seeds.
O There is statistically insignificant evidence to conclude that a plant that produces more seeds
will have seeds with a lower sprout rate than a plant that produces fewer seeds.
O There is statistically significant evidence to conclude that there is a correlation between the
number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the
regression line is useful.
d. r2 =
(Round to two decimal places)
e. Interpret r:
O 53% of all plants produce seeds whose chance of sprouting is the average chance of sprouting.
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