Question

Suppose a researcher is testing the hypothesis Upper H 0​: pequals0.4 versus Upper H 1​: pless than0.4 and she finds the​ P-value to be 0.33. Explain what this means. Would she reject the null​ hypothesis? Why? Choose the correct explanation below. A. If the​ P-value for a particular test statistic is 0.33​, she expects results no more extreme than the test statistic in about 33 of 100 samples if the null hypothesis is true. B. If the​ P-value for a particular test statistic is 0.33​, she expects results no more extreme than the test statistic in exactly 33 of 100 samples if the null hypothesis is true. C. If the​ P-value for a particular test statistic is 0.33​, she expects results at least as extreme as the test statistic in about 33 of 100 samples if the null hypothesis is true. D. If the​ P-value for a particular test statistic is 0.33​, she expects results at least as extreme as the test statistic in exactly 33 of 100 samples if the null hypothesis is true. Choose the correct conclusion below. A. Since this event is​ unusual, she will reject the null hypothesis. B. Since this event is not​ unusual, she will reject the null hypothesis. C. Since this event is​ unusual, she will not reject the null hypothesis. D. Since this event is not​ unusual, she will not reject the null hypothesis.

Answer 1

Answer:

D. If the​ P-value for a particular test statistic is 0.33​, she expects results at least as extreme as the test statistic in exactly 33 of 100 samples if the null hypothesis is true.

D. Since this event is not​ unusual, she will not reject the null hypothesis.

Step-by-step explanation:

Hello!

You have the following hypothesis:

H₀: ρ = 0.4

H₁: ρ < 0.4

Calculated p-value: 0.33

Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

In this case, you have a 33% chance of getting a value as extreme as the statistic value if the null hypothesis is true. In other words, you would expect results as extreme as the calculated statistic in 33 about 100 samples if the null hypothesis is true.

You didn't exactly specify a level of significance for the test, so, I'll use the most common one to make a decision: α: 0.05

Remember:

If p-value ≤ α, then you reject the null hypothesis.

If p-value > α, then you do not reject the null hypothesis.

Since 0.33 > 0.05 then I'll support the null hypothesis.

I hope it helps!