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goblinko [34]
3 years ago
13

From an industrial area 70 companies were selected at random and 45 of them were panning for expansion next year. Find 95% confi

dence limit for the proportion of companies planning for expansion?
Mathematics
1 answer:
Lana71 [14]3 years ago
8 0

Answer:

Confidence limit = [52.8%, 75.2%]

Step-by-step explanation:

P=\frac{45}{70}= 0.64

(1-P)=1-0.64=0.36

n= 70

P ± z \sqrt{\frac{P(1-P)}{n} }

where the value z will be taken from the z-table for 95% confidence interval

1-0.95= 0.05/2= 0.025

0.95+0.025= 0.0975

From the z-table the value of z corresponding to 0.0975 is 1.96

0.64 ± 1.96 \sqrt{\frac{0.64*0.36}{70} }

0.64 ± 1.96 (0.057)

0.64 ± 0.112

64%% ± 11.2%

so the confidence interval is

64+11.2=75.2%

64-11.2=52.8%

[52.8, 75.2]

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