MATH SOLVE

2 months ago

Q:
# Refer to the Current Allergy & Clinical Immunology (March 2004) study of latex allergy in health care workers. There is a claim that the mean number of latex gloves used per day by all hospital employees is less than 20 gloves. A sample of 46 were selected with a mean number of latex gloves used per day by all hospital employees of 19.3 and standard deviation of 11.9. Assume alpha is 0.01. What is the rejection region?a. z<-2.575 b. z<-2.33 c. z >2.575 d. z>2.33

Accepted Solution

A:

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 < 20A 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 ≥ 20H₁: μ < 20α: 0.01The 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!