Question

The historical average temperature in Newyork in July is 82° F. A meteorologist wants to know if the average temperature is higher now. They collect a sample of 10 July temperature averages and found an average temperature of 84° F with a standard deviation of 5. At the 1% significance level, is the average temperature in July higher now? Assume all CLT conditions hold. The hypotheses, test statistic, and p-value are below. Choose the correct conclusion.

H₀: μ = 82
H₁: μ > 82

Right tailed test

α = 0.01

t = 1.581

0.05 < p-val < 0.10

		The p-val is less than α, so reject H0. We don't have the evidence to conclude that the average temperature in July is higher now.
		The p-val is not less than α, so do not reject H0. We don't have the evidence to conclude that the average temperature in July is higher now.
		The p-val is less than α, so reject H0. We have the evidence to conclude that the average temperature in July is higher now.
		The p-val is not less than α, so reject H0. We have the evidence to conclude that the average temperature in July is higher now.

Answer 1

The p-value is not less than α, so do not reject H₀. We don't have the evidence to conclude that the average temperature in July is higher now.

Explanation:

For the given test scenario, we are given

0.05 < P-value < 0.10

Level of significance = α = 0.01

So, P-value > α = 0.01

So, we do not reject the null hypothesis at 1% level of significance.

The p-value is not less than α, so do not reject H₀. We don't have the evidence to conclude that the average temperature in July is higher now.