As the population s.d is known here, so we can use standard normal z table to estimate the answers.
Critical value z from z table for 99% confidence level is 2.576
Margin of error (MOE) = z*s.d/√n
0.15 = 2.576*0.15/√n
N = 74.
Null hypothesis Ho : u = 27.6
Alternate hypothesis Ha : u < 27.6
Margin of error (MOE) = z*s.d/√n = 2.576*0.5/√84 = 0.14053232131
Interval is given by,
(Mean - MOE, Mean + MOE).
As the interval contain the null hypothesised value 27.6 in it.
We fail to reject the null hypothesis Ho.
So, we do not have enough evidence to conclude that the population mean could be less than 27.6 inches.
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