Question

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 4949 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 overbar equals 19.2x=19.2 and s equals 11.7 .s=11.7. Complete parts (a)minus??(d).

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.

(?,?)

?(Use integers or decimals for any numbers in the expression. Round to two decimal places as? needed.)

c. Give a practical interpretation of the? interval, part? (b).

A.One can be? 95% confident that the average number of latex gloves used per week by all healthcare workers with a latex allergy is in the interval.

B.One can be? 95% confident that the average number of latex gloves used per week by all healthcare workers with a latex allergy is greater than the upper boundary of the interval.

C.One can be? 95% confident that the average number of latex gloves used per week by all healthcare workers with a latex allergy is less than the lower boundary of the interval.

D.One can be? 95% confident that latex gloves cause allergies for all who use a number of gloves contained in the interval.

d. Give conditions required for the? interval, part? (b), to be valid.

A.i. The sample selected was randomly selected from the target population.ii. The sample size is sufficiently? large, that? is,n>30

B.i. The sample selected was randomly selected from the target population.ii. The sample size is sufficiently? large, that? is,n>1000

C.i. The sample selected was specifically selected from the target population.ii. The sample size is sufficiently? large, that? is,n>1000

D.i. The sample selected was specifically selected from the target population.ii. The sample size is sufficiently? large, that? is,n>30

Answer 1

a.
Point estimate for the average number of latex gloves used per week = = 19.2

b.

Degree of freedom = n - 1 = 49 - 1 = 48

t value for 95% confidence interval and DF = 48 is 2.01

Standard error of sample mean = s / = 11.7 / = 1.671429

Margin of error = Standard error * t = 1.671429 * 2.01 = 3.359572

95% confidence interval is

(Point Estimate - Margin of error, Point Estimate + Margin of error)

(19.2 - 3.359572, 19.2 + 3.359572)

(15.84 , 22.56)

c.

The interpretation of 95% confidence interval is

A.One can be? 95% confident that the average number of latex gloves used per week by all healthcare workers with a latex allergy is in the interval.

d.

For 95% confidence interval to be valid,

A.i. The sample selected was randomly selected from the target population.ii. The sample size is sufficiently? large, that? is,n>30