Question

When testing whether the correlation coefficient differs from zero, the value of the test statistic is t20 = 1.95 with a corresponding p-value of 0.0653. At the 5% significance level (p = 0.05), can you conclude that the correlation coefficient differs from zero?
a) No, since the p-value exceeds 0.05. b) Yes, since the test statistic value of 1.95 exceeds 0.05. c) No, since the test statistic value of 1.95 exceeds 0.05. d) Yes, since the p-value exceeds 0.05.

Answer 1

No, we can't conclude that the correlation coefficient differs from zero because the p-value, which is 0.0653 exceeds 0.05. The correct option is a.

Given that:

p-value  = 0.0653                        

Level of significance (p) = 0.05  

The null hypothesis is a typical statical theory that suggests that no statical relationship and significance exists in a set of given single observed variables, between two sets of observed data and measured phenomena.

The null hypothesis is significant because it offers a rough description of the phenomena inferred from the available evidence. It enables researchers to empirically test the relationship statement in a study.

Example: The null hypothesis is that the population density is the same across all states.

The hypothesis is

H0: p=0 vs HA: p $\neq$ 0

We observe that,

p-value > p (level of significance)

So, fail to reject the null hypothesis (H0).

The correlation coefficient differs from zero when the p-value is less than 0.05.

Therefore, we can not conclude that the correlation coefficient differs from zero.

To learn more about the null hypothesis visit: https://brainly.com/question/28920252

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