It is important that face masks used by firefighters be able to withstand high t

Question

It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work in temperatures of 200-500°F. In a test of one type of mask, 11 of 55 masks had lenses pop out at 250°. Construct a 90% upper confidence limit for the true proportion of masks of this type whose lenses would pop out at 250°. (Round your answers to four decimal places.)

(__________,_________)

0.1113 Incorrect: Your answer is incorrect. , 0.2887 Incorrect: Your answer is incorrect.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

Here we have to find 90% confidence interval for the true proportion of masks of this type whose lenses would pop out at 250°.

Given values are :

n = 55

x = 11

c = confidence level = 90% = 0.90

90% confidence interval for true proportion is,

p^ - E < P < p^ + E

where p^ = x/n = 11/55 = 0.2

q^ = 1 - p^ = 1 - 0.2 = 0.8

E is margin of error.

E = Zc * sqrt( ( p^*q^) / n)

Zc we can find by using EXCEL.

syntax is,

=NORMSINV(probability)

where probability = 1 - a/2

where a = 1-c

Zc = 1.645

sqrt((p^*q^)/n) = sqrt((0.2*0.8) / 55) = sqrt(0.0029) = 0.0539

E = (1.645*0.0539) = 0.0887

lower limit = p^ - E = 0.2 - 0.0887 = 0.1113

upper limit = p^ + E = 0.2 + 0.0887 = 0.2887

This we can done using TI-83 calculator :

steps :

STAT --> TESTS --> A : 1-PropZInt --> Input x,n and C-level --> Calculate --> ENTER

Output is : (0.1113, 0.2887).

90% confidence interval for true population proportion is (0.1113, 0.2887).

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.