At a solar energy research station in Arizona, it was found that the mean number

Question

At a solar energy research station in Arizona, it was found that the mean number of BTU's absorbed by a particular solar panel was 18.5 BTU's. Suppose a random sample of 60 such panels yields an average of 17.4 BTU's with standard deviation 4.3 BTU's. Someone could look at this new sample data and decide that the mean number of BTU's is not what the research station claimed. Let's test this in two ways: Using the data from the sample, a) Find a 99 % confidence interval for the true mean number of BTU's b) Use a .01 level of significance to test the claim that the mean number #9) of BTU's is different than the original claim of 18.5 BTU's What do parts a) and b) indicate? Explain. Would the result of the hypothesis test be different if we used a.05 level of significance instead of.01? Explain. c) d)

Explanation / Answer

a)
z value at 99% = 2.576

CI = mean +/- z *(s/sqrt(n))
= 17.4 +/- 2.576 *(4.3/sqrt(60))
= (15.9701 , 18.8299 )

b)

Hypothesis:

H0 : mu = 18.5
Ha : mu not equals to 18.5

Test statistics:

z = ( x - mean)/(s/sqrt(n))
= ( 17.4 - 18.5)/(4.3/sqrt(60))
= -1.9815

p value = 0.0475

Do not reject the null hypothesis

c)

The a) part indicates that te 99% Ci falls between (15.9701 , 18.8299 )

and part b) indicates that the do not reject te null hypothesis

d)
We reject the null hypothesis because p value is greater than significance level

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