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(CO 7) A travel analyst claims that the mean room rates at a threestar hotel in Chicago is greater than $152. In a random sample of 36 threestar hotel rooms in Chicago, the mean room rate is $163 with a standard deviation of $41. At α=0.10, what type of test is this and can you support the analyst’s claim using the pvalue?
Claim is the alternative, fail to reject the null as pvalue (0.054) is less than alpha (0.10), and can support the claim 
Claim is the null, fail to reject the null as pvalue (0.054) is less than alpha (0.10), and cannot support the claim 
Claim is the alternative, reject the null as pvalue (0.054) is less than alpha (0.10), and can support the claim 
Claim is the null, reject the null as pvalue (0.054) is less than alpha (0.10), and cannot support the claim 2. (CO7) A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon. A random sample of 7 cars has a mean gas mileage of 23 miles per gallon and a standard deviation of 1.2 miles per gallon. At α=0.05, can you support the company’s claim?

Solution:
1) Claim is the alternative, reject the null as pvalue (0.054) is less than alpha (0.10), and can support the claim.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u < 152
Alternative hypothesis: u > 152
Note that these hypotheses constitute a onetailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a onesample ztest.
Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).
SE = s / sqrt(n)
S.E = 6.8333
z = (x  u) / SE
z = 1.61
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a z statistic test statistic of 1.61.
Thus the Pvalue in this analysis is 0.054.
Interpret results. Since the Pvalue (0.054) is less than the significance level (0.10), we have to reject the null hypothesis.
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