For this test, do the following.
(a) Identify the claim and state H0 and Ha.
(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning.
(c) Choose one of the options. If convenient, use technology.
Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic.
Option 2: Find the appropriate standardized test statistic and the P-value.
(d) Decide whether to reject or fail to reject the null hypothesis.
(e) Interpret the decision in the context of the original claim.
3. A travel agent says that the mean hotel room rate for a family of 4 in a certain resort town is at most $170. A random sample of 33 hotel room rates for families of 4 has a mean of $179 and a standard deviation of $19. At a = 0.01, is there enough evidence to reject the agent’s claim?
(a) The following null and alternative hypotheses need to be tested:
"H_0:\\mu\\le170"
"H_1:\\mu>170"
(b) This corresponds to a rightt-tailed one-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.
(c) Based on the information provided, the significance level is "\\alpha = 0.05," "df=n-1=32" degrees of freedom, and the critical value for a right-tailed test is "t_c = 1.693889."
The rejection region for this right-tailed test is "R = \\{t:t>1.693889\\}."
The t-statistic is computed as follows:
(d) Since it is observed that "t=2.7211>1.693889=t_c," it is then concluded that the null hypothesis is rejected.
Using the P-value approach:
The p-value for right-tailed, "df=32" degrees of freedom, "t=2.7211," is "p=0.005218\n," and since "p= 0.005218\n<0.05=\\alpha," it is concluded that the null hypothesis is rejected.
(e) Therefore, there is enough evidence to claim that the population mean "\\mu"
is greater than 170, at the "\\alpha = 0.05" significance level.
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