Question

In: Statistics and Probability

A survey of 542 consumers reveals that 301 favor the new design for a product. Construct...

A survey of 542 consumers reveals that 301 favor the new design for a product. Construct a 90% confidence interval for the true proportion of all consumers who favor the design.

Group of answer choices

0.514 < p < 0.597

0.522 < p < 0.588

0.520 < p < 0.591

0.500 < p < 0.610

0.518 < p < 0.593

Solutions

Expert Solution

Solution :

Given that,

n = 542

x = 301

Point estimate = sample proportion = = x / n = 301/542=0.555

1 -   = 1-0.555 =0.445

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E Z/2 *(( * (1 - )) / n)

= 1.645 *((0.555*0.445) /542 )

E = 0.035

A 90% confidence interval for proportion p is ,

- E < p < + E

0.555-0.035 < p < 0.555+0.035

0.520 < p < 0.591

orchestra answered 2 years ago
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