Question

In hypothesis testing, Yuka believes that the mean temperature in her town is 14.3°C. Hiroki, on the other hand, thinks it is higher. What is the null hypothesis (H0) for this t-test?

A) H0: μ ≤ 14.3°C
B) H0: μ > 14.3°C
C) H0: μ = 14.3°C
D) H0: μ < 14.3°C

Answer 1

The correct null hypothesis (H0) for the described t-test, where Yuka believes the mean temperature is 14.3°C but Hiroki believes it is higher, is H0: μ = 14.3°C.

Step-by-step explanation:

The null hypothesis (H0) in hypothesis testing is a statement that there is no effect or no difference, and it is the hypothesis that is subject to testing. In the case where Yuka believes that the mean temperature in her town is 14.3°C and Hiroki thinks it is higher, the null hypothesis should reflect the assumption that there is no difference from the claimed mean, so it would set the mean as equal to 14.3°C. Therefore, the correct null hypothesis (H0) for this t-test would be:

• H0: μ = 14.3°C

This hypothesis is chosen because it is the statement that there is no difference from 14.3°C, which is what we are testing against. If the data provides sufficient evidence to suggest that the mean is greater than 14.3°C, we would reject the null hypothesis in favor of Hiroki's belief that the mean temperature is higher.