Answer
Yes, see explanations.
Work Step by Step
a. State the hypotheses and identify the claim.
$H_o: \mu_D\leq 10$
$H_a: \mu_D \gt 10$ (claim, right tail test)
b. Find the critical value(s).
$\alpha=0.01, df=9, t_c=2.821$
c. Compute the test value.
$n=10, \sum D=176, \bar D=17.6, \sum D^2=3590$,
$S_D=\sqrt {\frac{10\times3590-176^2}{10\times9}}=7.4, t=\frac{17.6-10}{7.4/\sqrt {10}}=3.25$
d. Make the decision.
Since $t\gt t_c$, we reject the null hypothesis.
e. Summarize the results.
At the 0.01 level of significance, there is sufficient evidence to conclude that there is more than
a 10$^\circ$ difference between average highs and lows.
