Question

Suppose you have the following null and alternative hypotheses: H0 : μ = 8.3 and H1 : μ ≠ 8.3. You take a sample of 25 observations, and find a sample mean of 7.3 with a standard deviation of 3.2. Which of the following is the most accurate statement about the p-value?

A.

0.05 < p-value < 0.10

B.

p-value < 0.01

C.

0.01 < p-value < 0.05

D.

p-value > 0.10

Answer 1

Ans: The significance level for a given hypothesis test is a value for which a P-value less than or equal to is considered statistically significant. Typical values for are 0.1, 0.05, and 0.01. These values correspond to the probability of observing such an extreme value by chance.

The choice of significance level at which you reject H₀ is arbitrary. Conventionally the 5% (less than 1 in 20 chance of being wrong), 1% and 0.1% (P < 0.05, 0.01 and0.001) levels have been used. These numbers can give a false sense of security. ... The significance level (alpha) is the probability of type I error.

p-value helps you determine the significance of your results. ... A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

The most accurate statement about the p-value

B. p-value<0.01