Homework question. Please give me the right answer!! To select the site for an e
ID: 3255929 • Letter: H
Question
Homework question.
Please give me the right answer!!
To select the site for an electricity-generating wind turbine, wind speeds were recorded at several potential sites every six hours for a year Two sites not far from each other qualify, but we should choose the site with a higher average daily wind speed. Because the sites are near each other and the wind speeds were recorded at the same times, we should view the speeds as paired. Test an appropriate hypothesis to see if there is evidence that either of these sites has a higher average wind speed. Note that all assumptions and conditions for inference on this data have been satisfied EE Click the icon to view the results. Find the t statistic and P-value for this test of hypothesis then state the conclusion. Calculate t. (Round to three decimal places as needed.)Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 = 2
Alternative hypothesis: 1 2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.150
DF = 2226
t = [ (x1 - x2) - d ] / SE
t = - 1.2333
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 2226 degrees of freedom is more extreme than -1.233; that is, less than -1.233 or greater than 1.233.
Thus, the P-value = 0.218
Interpret results. Since the P-value (0.218) is greater than the significance level (0.05), we have to accept the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that either of these sites has higher average wind speed.
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