Question

SOLVE FOR CHILDRENS HOSPITAL OF DESTIN. A. GIVE A POINT ESTIMATE FOR THE AVERAGE NUMBER OF LATEX GLOVES USED PER WEEK BY ALL HEALTH CARE WORKERS WITH A LATEX ALLERGY.

Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each in a sample of 49 hospital employees who were diagnosed with a latex allergy based on a skin-prick test reported on their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are x = 19.5 and s = 12.3. Complete parts (a) – (d).

B. FROM A 95% CONFIDENCE INTERVAL FOR THE AVERAGE NUMBER OF LATEX GLOVES USED PER WEEK BY ALL HEALTH CARE WORKERS WITH A LATEX ALLERGY.

Answer 1

Question 1

Part a)

Point Estimate  X̅ = 19.5

Part b)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 49- 1 ) = 2.011 ( From t table )
19.5 ± t(0.05/2, 49 -1) * 12.3/√(49)
Lower Limit = 19.5 - t(0.05/2, 49 -1) 12.3/√(49)
Lower Limit = 15.9664
Upper Limit = 19.5 + t(0.05/2, 49 -1) 12.3/√(49)
Upper Limit = 23.0336
95% Confidence interval is ( 15.9664 , 23.0336 )

Question 2

Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )
Z(α/2) = Z (0.1 /2) = 1.645 ( From Z table )
7.62 ± Z (0.1/2 ) * 8.94/√(61)
Lower Limit = 7.62 - Z(0.1/2) 8.94/√(61)
Lower Limit = 5.74
Upper Limit = 7.62 + Z(0.1/2) 8.94/√(61)
Upper Limit = 9.50
90% Confidence interval is ( 5.74 , 9.50 )