Question

Suppose you carry out a significance test of H0: μ = 3.5 versus Ha: μ < 3.5 based on sample size n = 17 and obtain t = –3.4. Find the p-value for this test. What conclusion can you draw at the 5% significance level? Explain.a. The p-value is 0.4982. We reject H0 at the 5% significance level because the p-value 0.4982 is greater than 0.05.b. The p-value is 0.4982. We fail to reject H0 at the 5% significance level because the p-value 0.4982 is greater than 0.05.c. The p-value is 0.5018. We fail to reject H0 at the 5% significance level because the p-value 0.5018 is greater than 0.05.d. The p-value is 0.0018. We reject H0 at the 5% significance level because the p-value 0.0018 is less than 0.05.e. The p-value is 0.0018. We fail to reject H0 at the 5% significance level because the p-value 0.0018 is less than 0.05.

Answer 1

Answer:

We reject H0 at the 5% significance level because the p-value 0.0018 is less than 0.05 is the correct answer here.

Step-by-step explanation:

For n - 1= 16 degrees of freedom, we get from the t distribution tables for this one tailed test the p-value as:

p = P( t16 < -3.4) = 0.0018

As the p-value here is 0.0018 < 0.05 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here. Therefore The p-value is 0.0018. We reject H0 at the 5% significance level because the p-value 0.0018 is less than 0.05 is the correct answer here.

Answer 2

The conclusion about the signifucance level is that D. We reject H0 at the 5% significance level because the p-value 0.0018 is less than 0.05.

What is a significance level?

The significance level of an event is the probability that the event could have occurred by chance.

Here, we get from the t distribution tables for this one tailed test as: p = P( t16 < -3.4) = 0.0018

Therefore, the p-value is 0.0018, hence, we reject H0 at the 5% significance level.

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