Answer:
Step-by-step explanation:
Hello!
The researcher wants to test if the average number of latex gloves used per day by all hospital employees is less than 20, symbolically: μ < 20
A sample of 46 workers was selected and a sample means of X[bar]= 19.3 and a sample standard deviation of S= 11.9.
The study variable is X: number of latex gloves used per day by a hospital employee.
There is no information about the variable distribution, but since the sample is large enough (n≥30) we can apply the Central Limit Theorem and approximate the distribution of the sample mean to normal X[bar]≈N(μ;δ²/n)
The hypotheses are:
H₀: μ ≥ 20
H₁: μ < 20
α: 0.01
The statistic to use is the standard normal approximation:
[tex]Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } }[/tex]
[tex]Z_{H_0}= \frac{19.3-20}{\frac{11.9}{\sqrt{46} } }= -0.398 = -0.4[/tex]
With critical level [tex]Z_{\alpha } = Z_{0.01} = -2.334[/tex], considering the test is one-tailed left, the calculated Z value is greater than the critical value so the decision is to not reject the null hypothesis.
I hope it helps!
