Arandom sample of 32 days for the three gorges dam in china provides an average of 266.8 gigawatts of power produced per day with a standard deviation of 22 gigawatts. (a) compute a 95% confidence interval for the true mean power per day. is 274 gigawatts a plausible value for µ? explain. (b) complete a hypothesis test at α = 0.05 to test µ = 274 versus µ 6= 274. (c) are the results from (a) and (b) consistent (i. e., do you get the same conclusion from both)?

a) The 95% CI for the mean is .

The value 274 is plausible because it is within the limits of the CI.

b) We can not reject the hypothesis

c) They are consistent. The conclusion from both results is that 274 could be the real mean. In both cases we couldn't prove 274 it is not the mean.

Step-by-step explanation:

In this problem we have a sample of n=32 with mean M=266.8 and standard deviation s=22.

a) To compute a 95% confidence interval (CI), we calculate

First we have to estimate t, with 32-1=31 degrees of freedom for a two-tailed 95% CI.

By looking up in the t-table, we get t=2.0395.

Then the confidence interval is

b) We have to test the hypothesis

The significance level is 0.05.

We calculate the t-statistics:

The p-value for t=1.84 and df=31 is P=0.07536.

As P=0.07 is greater than the significance level (0.05), we can not reject the null hypothesis. The interpretation of this is we can not claim that the mean is not 274.

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the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap