Question

hours dogs sleep the canadian press reported that dogs sleep on average 14 hours per day. a veterinarian studied a random sample of 20 dogs and found that they sleep on average 14.7 hours. the standard deviation of the population, which was 1.7 hours, was found from previous studies. at \\( \alpha = 0.01 \\), can it be concluded that on average dogs sleep more than 14 hours per day? assume the variable is normally distributed. use the critical value method.
part 1 of 5
(a) state the hypotheses and identify the claim with the correct hypothesis.
\\( h _ { 0 } : \mu = 14 \\) not claim
\\( h _ { 1 } : \mu > 14 \\) claim
this hypothesis test is a one-tailed test.
part: 1 / 5
part 2 of 5
(b) find the critical value(s). round the answer(s) to at least two decimal places. if there is more than one critical value, separate them with commas.
critical value(s):

Explanation:

Step1: Determine the type of distribution

Since the population standard deviation $\sigma = 1.7$ is known and the sample size $n=20$, and the variable is normally distributed, we use the standard - normal ($z$) distribution for hypothesis testing.

Step2: Recall the formula for the critical value in a right - tailed test

For a right - tailed test with significance level $\alpha = 0.01$, we look up the $z$ - value in the standard - normal distribution table. The critical value $z_{\alpha}$ is the value such that $P(Z>z_{\alpha})=\alpha$.
Using the standard - normal distribution table or a calculator with a normal - distribution function (e.g., in Excel, we can use the formula =NORM.S.INV(1 - 0.01)), we find that the critical value for a right - tailed test with $\alpha = 0.01$ is $z_{0.01}=2.33$.

Answer:

$2.33$