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Question

# 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 $$ \overline { x } = 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.

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1 of 5Given:

$\overline{x}=19.3$

$s=11.9$

$n=46$

$c=95\%=0.95$

The sample is large (sample size of at least 30) and thus it is safe to assume that the population standard deviation $\sigma$ is approximately equal to the sample standard deviation $s$:

$\sigma\approx s=11.9$

(a) A point estimate for the average is given by the sample mean $\overline{x}$:

$\overline{x}=19.3$

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