Answer:
32 days must be sampled to test the proposed hypothesis.
Step-by-step explanation:
Consider the provided information.
The average number of person-hours per day spent on these task was [tex]\mu_0=16[/tex].
The actual value of μ is 12 hours or less i.e μ=12
She wants a test having α=0.05
The probability of a type II error of at most β=0.10 and σ=7.64.
δ = μ-μ0
= 12-16
= -4
Now use the formula for calculating the sample size:
[tex]N=\frac{(Z_{\alpha}+Z_{\beta})^2\sigma^2}{\delta^2}[/tex]
Substitute the respective values.
[tex]N=\frac{(Z_{0.05}+Z_{0.1})^2(7.64)^2}{(-4)^2}[/tex]
[tex]N=\frac{(1.6449+1.2816)^2(7.64)^2}{16}[/tex]
[tex]N=31.2437958482\approx 32[/tex]
Hence, 32 days must be sampled to test the proposed hypothesis.
