Latex allergy in health care workers. Refer to the Current Allergy & Clinical Immunology (March 2004) study of n = 46 hospital employees who were diagnosed with a latex allergy from exposure to the powder on latex gloves, presented in Exercise 8.28 (p. 365). Recall that the number of latex gloves used per week by the sampled workers is summarized as follows:  = 19.3 and s = 11.9. Let σ² represent the variance in the number of latex gloves used per week by all hospital employees. Consider testing H₀: σ² = 100 against H_a: σ² ≠ 100.

a. Give the rejection region for the test at a significance level of a = .01.

b. Calculate the value of the test statistic.

c. Use the results from parts a and b to draw the appropriate conclusion.

Exercise 8.28

Latex allergy in health care workers. Refer to the Current Allergy & Clinical Immunology (March 2004) study of n = 46 hospital employees who were diagnosed with a latex allergy from exposure to the powder on latex gloves, presented in Exercise 7.13 (p. 307). The number of latex gloves used per week by the sampled workers is summarized as follows:   = 19.3 and s = 11.9. Let μ represent the mean number of latex gloves used per week by all hospital employees. Consider testing H₀: μ = 20 against H_a: μ

a. Give the rejection region for the test at a significance level of a = .01.

b. Calculate the value of the test statistic.

c. Use the results from parts a and b to draw the appropriate conclusion.

Exercise 7.13

Latex allergy in health care workers. Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Symptoms of a latex allergy include conjunctivitis, hand eczema, nasal congestion, a skin rash, and shortness of breath. Each in a sample of 46 hospital employees who were diagnosed with latex allergy based on a skin-prick test reported on their exposure to latex gloves (Current Allergy & Clinical Immunology, March 2004). Summary statistics for the number of latex gloves used per week are  = 19.3 and s = 11.9.

a. Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy.

b. Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy.

c. Give a practical interpretation of the interval you found in part b.

d. Give the conditions required for the interval in part b to be valid.