Suppose you will perform a test to determine whether there is sufficient evidence to support a
1 answer:
Answer:
The critical values of r are -0.708 and 0.708.
Step-by-step explanation:
A statistical test is being performed to determine whether there is any linear correlation between two variables.
The hypothesis can be defined as follows:
<em>H</em>₀: There is no linear correlation between two variables, i.e. <em>ρ</em> = 0.
<em>H</em>ₐ: There is a significant linear correlation between two variables, i.e. <em>ρ</em> ≠ 0.
The test statistic is given as follows:
The degrees of freedom of the test is:
The significance level of the test is, <em>α</em> = 0.01.
The critical values of <em>r</em> are:
*Use the <em>r</em> critical value table.
Thus, the critical values of r are -0.708 and 0.708.
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Using the z-distribution, since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.
<h3>What are the hypotheses tested?</h3>At the null hypotheses, we test if the proportion of successes equals 0.5, hence:
At the alternative hypotheses, we test if it does not equal, hence:
The test statistic is given by:
In which:
is the sample proportion.
- p is the proportion tested at the null hypothesis.
- n is the sample size.
For this problem, the parameters are given by:
Hence the test statistic is given by:
z = (0.35 - 0.5)/(0.5/sqrt(40))
z = -1.9.
<h3>What is the decision?</h3>Using a z-distribution calculator, considering a two-tailed test, as we are testing if the proportion is different of a value, with z = -1.9, we get that the p-value of the test is of 0.057.
Since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.
More can be learned about the z-distribution at brainly.com/question/16313918
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